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Irish Astr. J., 26, 91--93 (1999) [1999 July issue]
c
fl IAJ 1999 Last revised 1999 May 21
THE RESONANT LEONID TRAIL FROM 1333
D. J. ASHER & M. E. BAILEY
Armagh Observatory, College Hill, Armagh, BT61 9DG, U.K.
and
V. V. EMEL'YANENKO
Department of Theoretical Mechanics, South Ural University, Chelyabinsk, 454080, Russia
(E­mail dja@star.arm.ac.uk)
ABSTRACT. The largest contribution to the fireball­rich Leonid outburst of 1998 has
previously been shown to be a component of resonant meteoroids ejected from Comet
55P/Tempel­Tuttle in 1333. By integrating particles with a suitable range of initial or­
bits, we demonstrate here that the cross section of the arc of resonant particles from 1333
through which the Earth passed in 1998 is quite compact and reflects details of the particles'
initial ejection velocities. This is because resonant motion prevents streams of particles from
dispersing as quickly as non­resonant particles.
1. INTRODUCTION: TWO KINDS OF TRAIL
Enhanced meteor activity, sometimes to storm level, occurs when the Earth passes through a
narrow, dense trail of material within a meteoroid stream (Kres'ak 1993). Trails are normally
formed as meteoroids are ejected from a parent comet with orbital periods differing slightly
from that of the comet, gradually separating therefore in mean anomaly M .
A new trail in the Leonid stream is created each time Comet 55P/Tempel­Tuttle returns
to perihelion, every 33 years or so. The gravitational perturbations on these `normal' Leonid
trails, which vary as a function of position along the trail, can be evaluated and accurately
related to past Leonid storms, and used to predict those in future years (Kondrat'eva &
Reznikov 1985; Kondrat'eva et al. 1997; Asher 1999; McNaught & Asher 1999). However,
none of these young, normal trails explains the observed outburst (Arlt 1998) of Leonid
fireballs in 1998, which was noted for having a sharp maximum more than half a day before
the Earth's passage through the comet's orbital plane.
Progressively more of any given trail is scattered by planetary perturbations, and after
(say) a dozen revolutions the trail no longer exists as a single, coherent entity. The evolution
then depends more on long­term dynamics rather than there simply being a trail stretching
predominantly in M . Particles moving in Halley­type orbits often spend substantial phases
in mean motion resonances with Jupiter (Carusi et al. 1987; Asher et al. 1994; Chambers
1995). In the long term, two contrasting kinds of dynamical behaviour can be identified,
resonant and non­resonant, respectively characterised by near­regular and chaotic motion
(Emel'yanenko & Bailey 1996). In the former case, particles remain concentrated in smaller
regions of phase space, and moreover the motion is predictable over much longer timescales.
Particles displaying chaotic behaviour soon become widely scattered in space, whereas par­
ticles released into a resonance can remain in well defined trails for a significant time,
particularly particles larger than a few mm in diameter, which are relatively unaffected by
radiative forces. As these trails exist because of a long­term dynamical phenomenon, they
are distinct from the normal trails described above.
The fact that 55P/Tempel­Tuttle is in the 5/14 Jovian resonance, coupled with the
fact that evolution of resonant particles is predictable over considerably more than a few
centuries, led Asher et al. (1999) to suppose that the source of the 1998 outburst could
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be unambiguously identified. By examining all possibilities for ejection over the past 1400
years (42 revolutions), they found that a subset of particles ejected into the resonance in
1333 (20 revolutions ago), namely those within a small range of initial semi­major axis a 0
around 10.30 AU, evolved to be exactly capable of hitting the Earth in 1998. Furthermore,
the calculated time of impact perfectly matched the observed fireball peak, distinct from the
time of passage through the comet plane. A secondary solution, comprising particles ejected
in 1433, but with a substantially smaller density in 1998 compared to the 1333 substream,
was also found, with a calculated time two hours later. It too seems detectable in the data
(Figure 7 of Arlt 1998), albeit hardly above the noise level.
The calculated a 0 in 1333 relative to the comet was \Deltaa 0 ú \Gamma0:024 AU, corresponding
to a transverse ejection velocity around --2.4 m/s at perihelion. The value would become
more negative if the effect of radiation pressure were included (cf. Kondrat'eva & Reznikov
1985; Asher 1999). Because the frequency distribution of ejected particles tends to peak at
around a transverse velocity of zero, and with a broader spread for smaller particles, a lower
proportion of ejected particles of smaller size will have the necessary value of a 0 to give the
1998 Earth intersection. This explains why the outburst in question was rich in fireballs but
comparatively poor in faint meteors.
2. RESONANT TRAIL CROSS SECTION
The calculations in Asher et al. (1999) were done assuming ejection exactly at perihelion,
i.e., always near 1 AU. This was sufficient for calculating nominal nodal crossing points as
a function of a 0 and time of ejection from 1 to 42 revolutions ago, and allowed 1333 and
the appropriate a 0 to be found. However, as nodal crossing occurs near perihelion, particles
ejected at perihelion with a range of velocities have a negligible dispersion at their node.
In reality, volatiles are released from the nucleus at heliocentric distances r up to at least
2 AU, perhaps significantly more. We have therefore carried out a numerical simulation to
investigate the cross­sectional dispersion caused by ejection over a more realistic range than
at perihelion only.
Isotropic ejection at the 1333 epoch was considered, with 1/r velocity dependence. Ejec­
tion was assumed to be uniform in true anomaly between --120 ffi and +120 ffi , or r ! 3.4
AU, and zero outside this range (cf. Brown & Jones 1998). Particles were generated using
a Monte Carlo program, discarding them unless \Gamma0:029 ! \Deltaa 0 ! \Gamma0:019. The remaining
particles were integrated forward to 1998 using gravitational forces (sun and 8 main plan­
ets) only. It was known from Asher et al. (1999) that particles with \Deltaa 0 outside that range
would not give the desired Earth intersection in 1998.
Since one component of the ejection velocity has magnitude 2.4 m/s, the required overall
ejection velocity at perihelion is at least this. Figures 1 and 2 show results assuming the
ejection speed at 1 AU to be respectively 10 and 20 m/s. Not all the integrated particles
have been plotted, rather only those with the correct mean anomaly M in 1998 to pass
through the ecliptic when the Earth was in the vicinity. Specifically, a range of 0.03 ffi in
M has been used, bracketing the correct value. Further subdividing the particles on the
basis of M does not change the cross­sectional distributions. The plotted particles, while
constituting just under 10% of the integrated particles, all had \Gamma0:026 ! \Deltaa 0 ! \Gamma0:021,
verifying that a sufficient range had been integrated.
The Figures show that a dispersion equivalent to between one and a few hours in longi­
tude (i.e. !
¸ 0.1 ffi ) for the chosen ejection speeds, is induced entirely as a result of ejection.
Gravitational perturbations have shifted the nodal crossing of the `resonant arc' to a very
different (x,y) by 1998, but differential perturbations among the particles are small and
have not increased the dispersion in longitude at all. The radial dispersion has increased
a little, though not much, over the course of seven centuries. This lack of dispersion is a
consequence of the regular nature of resonant orbits (Emel'yanenko and Bailey 1996).
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Figure 1: Ecliptic cross section of resonant trail, shown at ejection epoch and at time of
Earth encounter. Descending nodes are plotted of particles ejected in 1333 that have the
correct mean anomaly to cross the ecliptic when the Earth is nearby in 1998. The x and y
axis scales are in AU. Ejection speed 10 m/s at heliocentric distance r = 1 AU, falling as
1/r. Cross is comet's descending node in 1333 and line is Earth's orbit in 1998.
3. CONCLUSION
The Infra­Red Astronomical Satellite discovered a large number of dust trails with no known
parent comet (Sykes et al. 1986). One possible explanation for these `orphan trails' is that
they are formed by resonant particles. Separation from their parent object long ago would
explain the lack of a present association with a comet, but the resonant mechanism would
enable the trail structure to be maintained over that time. Here, for the Leonids, we have
verified using integrations that a resonant arc of particles can exist whose width is of the
same order as it was at the time of ejection. Therefore for outbursts resulting from particular
resonant arcs, such as with the 1998 fireballs, the activity profile for the observed meteor
shower largely reflects the details of ejection from the comet.
Acknowledgements
We are grateful to John Chambers for the use of his Mercury integrator package.
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Figure 2: As Figure 1 except that the ejection speed is 20/r instead of 10/r m/s.
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