Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~ambn/persevo.ps Äàòà èçìåíåíèÿ: Thu Oct 10 18:29:41 1996 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 21:29:44 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: trifid nebula

THE FORMATION AND EVOLUTION OF THE
PERSEID METEOROID STREAM
Nathan W. Harris 1;2
1 Astrophysics Research Group, School of Electrical Engineering,
Electronics & Physics, Liverpool John Moores University, Byrom Street,
Liverpool, L3 3AF, UK.
Abstract. The orbital evolution of two modelled `Perseid' meteoroid
streams is investigated using direct numerical integration techniques. We
conclude that, in the absence of significant meteoroid velocity determina­
tion errors, the observed meteoroid orbital semi­major axis distribution is
a direct consequence of the cometary ejection process and not due to sub­
sequent orbital evolution. A high ejection­velocity (¸ 0:6 km s \Gamma1 ) model
stream succeeds in reproducing the observations. Conclusions are made
concerning how the orbital stability of Earth­orbit­intersecting Perseid
meteoroids varies with initial orbital semi­major axis.
1. Introduction
A simple model has been developed to represent the formation of the Perseid
meteoroid stream by considering the way in which both the velocity of the me­
teoroids emitted from the surface of the parent cometary nucleus (109P/Swift­
Tuttle) and the number ejected per unit time vary as a function of heliocentric
distance and comet­Sun­meteoroid ejection angle (Harris et al. 1995). The IAU
Meteor Data Centre at Lund (Lindblad 1991) contains a large data set of me­
teoroid orbits which allows us to gain reliable information on the distribution
of the orbital elements for most of the major meteoroid streams. The D 0 crite­
rion (Drummond 1981) can be used to select Perseid stream members from the
stream candidates (e.g. Harris & Hughes 1995). The orbital semi­major axis
(a) distribution is shown in Figure 1 (i) (for a values up to 50 AU). There is
considerable spread in the observed a distribution, ranging from around 6 AU
to near parabolic orbits. The contribution to the observed (measured) spread
due to errors in the meteoroid velocity determination is unclear (the velocity
errors maybe as high as 1 %) and is therefore ignored in the following work.
This effect will be considered in a later paper. The distribution peak occurs be­
tween 12 and 18 AU whereas the cometary orbital semi­major axis is around 26
AU. The lower a (and hence lower orbital period) meteoroids, however, intersect
the Earth's orbit more frequently. An unbiased distribution could therefore be
determined by multiplying the number of meteoroids in each histogram a bin
by the corresponding orbital period. Figure 1 (ii) shows a plot of meteoroid
2 Present address : Armagh Observatory, College Hill, Armagh, Northern Ireland, BT61 9DG
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Figure 1. (i) The observed photographic Perseid meteoroid orbital
semi­major axis distribution. (ii) A plot of a versus the longitude of
the ascending node for the observed Perseid meteoroids.
a as a function of the longitude of the ascending
node,\Omega\Gamma The figure clearly
shows that there is no correlation between the two parameters indicating that
those meteoroids that happen to intersect the Earth's orbit (and can potentially
become visible as meteors) do not exhibit any special orbital semi­major axis
values.
2. Meteoroid Ejection and Orbital Evolution
Whipple's formula for the ejection velocity of meteoroids from a cometary nu­
cleus (Whipple 1951) results in an ejection velocity of order 0.05 km s \Gamma1 for
meteoriods capable of producing `typical' photographic Perseid meteors. (The
`typical' photographic Perseid meteor is caused by a meteoroid of mass ¸ 0:5 g
and density around 0.3 g cm \Gamma3 ). In comparison the observed gas expansion ve­
locities in cometary comae as a function of heliocentric distance is given by the
relationship V gas = 0:58r \Gamma0:5 , where V gas is in km s \Gamma1 and r is in AU (Delsemme
1982). At the perihelion distance of Swift­Tuttle, this results in a gas expansion
velocity of around 0.6 km s \Gamma1 . The solid­line histograms in Figure 2 show the
resulting modelled meteoroid a distributions produced by ejecting meteoroids
at perihelion, in the plane of the parent comet's orbit (according to the model
mentioned above), with a Maxwellian velocity distribution that peaks at a value
of 0.05 km s \Gamma1 , shown in Figure 2 (i) and 0.6 km s \Gamma1 , shown in Figure 2 (ii). The
cometary orbital parameters used were the mean values for the last 20 appari­
tions prior to 1862 (Yau et al. 1994). The high dust ejection velocities produce
an a distribution that resembles the observed distribution. The low dust ejec­
tion velocities produce an a distribution with 20 ! a ! 38 AU with a peak that
coincides with that of the parent comet at around 26.58 AU. Comparing this
with the observed distribution (Figure 1 (i)), it is clear that we require a mech­
anism for the systematic reduction of the modelled peak value to the observed
peak value and also considerable spreading out of the distribution to higher and
lower a values.
The Poynting­Robertson effect is one such possible mechanism. The orbital
lifetime of a `typical' Perseid stream meteoroid (with initial values of a and e
of 25 AU and 0.969 respectively) under the PR effect (i.e. the time it takes
the particle to spiral into the Sun) is approximately 2 \Theta 10 9 years (Wyatt &
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Figure 2. (i) Modelled meteoroid a distribution produced with mean
ejection velocity of 0.05 km s \Gamma1 (solid­line histogram). The dotted­
line histogram shows the corresponding meteoroid a distribution after
36000 years of gravitational perturbation. (ii) As for Figure 2 (i) but
mean ejection velocity is 0.6 km s \Gamma1 ; perturbation time is 28000 y.
Whipple 1950). For an initial a of 12 AU (e=0.92) the corresponding lifetime
is around 5 \Theta 10 8 years. As the collisional lifetime of a stream meteoroid is
generally thought to be of the order 10 5\Sigma1 years (Gr¨un et al. 1984; Steel &
Elford 1985) it is clear that the PR effect does not act swiftly enough to explain
the discrepancy between the model and the observations.
Another possibility is that the presently observed meteoroids were ejected
from a parent body with a around 12 to 18 AU. Orbital integrations of Swift­
Tuttle, however, indicate that a does not tend to decrease as we integrate back­
wards in time (Bailey & Emel'yanenko 1995).
3. Gravitational Perturbation and Conclusions
A third mechanism is the systematic reduction of meteoroid a due to gravita­
tional perturbations. The modelled stream (containing ¸ 1000 particles) was
evolved for a few \Theta10 4 years into the future using an orbital integration pro­
gram based on the RADAU subroutine written by Everhart (1985). All planets
from Earth to Neptune were taken into account and the masses of Mercury and
Venus were added to that of the Sun. The Earth and Moon were treated as a
single body. Figure 2 (i) (dotted­line histogram) shows the resulting meteoroid
a distribution after 36000 years of gravitational perturbation. It is evident that
the overall effect is one of a gradual spreading out of the distribution with little
movement in the distribution peak. This suggests that, in the absence of signif­
icant observational errors, the observed a distribution is a direct consequence of
meteoroid stream formation and not due to subsequent orbital evolution. This
conclusion requires meteoroids to be ejected with high velocities, corresponding
to model (ii). High ejection velocities could be obtained by massive meteoroids
if the particles have non­spherical shapes and a high surface­area­to­mass ratio
(Gustafson 1989). Figure 2 (ii) (dotted­line histogram) shows the meteoroid a
distribution for model (ii) after 28000 years of gravitational perturbation. The
distribution as a whole is relatively stable over this time period, the only ob­
vious movement being the `sorting out' into various mean­motion resonances
(mainly with Jupiter, eg. 1:n, where n=3,...7.) (cf. Wu and Williams 1995).
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Figure 3. Plots of the heliocentric distance of the descending node
(r dnode ) against a for specific epochs during the meteoroid stream evo­
lution.
Examination of Figure 3, however, indicates a correlation between the stream
dispersion rate and the initial meteoroid a. At time t=0 (i.e. soon after ejec­
tion) meteoroids with orbital descending nodes at the Earth's orbit, r dnode ' 1
AU, (i.e. those which can potentially be seen as meteors) are represented by
the whole spectrum of a values. As we follow the orbital evolution forwards it
is clear that the lower a meteoroids (a ! 15 AU) have their r dnode perturbed
to heliocentric distances lying outside the Earth's orbit over a much shorter
timescale than the higher a meteoroids. This means that the observed low a
meteoroids are relatively young and must have been ejected from the cometary
nucleus within the last few thousand years (! 50 cometary orbital periods). The
higher a meteoroids can have much longer observable lifetimes (? 10000 y).
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