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Mon. Not. R. Astron. Soc. 000, 000--000 (0000) Printed 9 March 1999 (MN L A T E X style file v1.4)
Resonant meteoroids from Comet Tempel­Tuttle in 1333:
the cause of the unexpected Leonid outburst in 1998
D.J. Asher 1? , M.E. Bailey 1 and V.V. Emel'yanenko 2
1 Armagh Observatory, College Hill, Armagh, BT61 9DG, U.K.
2 Department of Theoretical Mechanics, South Ural University, Chelyabinsk, 454080, Russia
Accepted 1999 March 9. Last update 1999 March 1; in original form 1999 January 11
ABSTRACT
Recent observations of an unexpectedly high incidence of bright Leonid meteors about
16 hours before the predicted maximum of the main shower are explained by the ejec­
tion of dust grains into the 5/14 mean­motion resonance with Jupiter, principally
during the perihelion passage of Comet 55P/Tempel­Tuttle in 1333. The dynamical
evolution of resonant grains has the following properties: first, they do not spread uni­
formly around the orbit, but instead librate about a resonance centre within the main
stream; secondly, these resonant zones contain a much higher space density of particles
than the background stream, with the particle density approaching that of recently
ejected cometary grains; and thirdly, differential precession between the cometary or­
bit and the orbits of resonant particles may lead to meteor storms at unexpected times,
possibly far removed from that of the normal shower. The presence of resonant dust
grains leads to a complex structure within the Leonid meteoroid stream, and is an
important general feature of meteoroid streams associated with Halley­type comets,
themselves often trapped for long periods in mean­motion resonances.
Key words: comets: individual: 55P/Tempel­Tuttle -- meteors, meteoroids -- Solar
system: general.
1 INTRODUCTION
The annual Leonid meteor shower occurs between approx­
imately 15 and 21 November each year, with a maximum
during 17/18 November. It is historically one of the best
known meteor showers, with records of meteor storms (vi­
sual meteor rates greater than 10 3 per hour) extending back
more than a thousand years to AD 899 (Astapovich 1968;
Katasev & Kulikova 1972; Yeomans 1981; Yeomans, Yau &
Weissman 1996). These episodes of very high meteor flux
usually occur within a few years of the perihelion passage of
the parent comet. Since Comet 55P/Tempel­Tuttle passed
perihelion on 1998 February 28, there was much interest in
the shower of 1998 and its implications for 1999 and 2000.
In the event, although predictions of the strength of the
1998 event (Brown & Jones 1996; Jenniskens 1996; Wu &
Williams 1996; Yeomans et al. 1996; Arlt, Molau & Currie
1998) were broadly vindicated, indicating a strong shower
but no storm, astronomers and other commentators were
surprised by a strong peak in the fireball flux more than
half a day earlier than expected. Whereas the normal max­
imum of the meteor storm component occurs close to solar
longitude (equinox J2000.0) – fi = 235: ffi 25 (1998 November
? E­mail: dja@star.arm.ac.uk
17.8), compared with the peak of the background non­storm
meteor shower at – fi ' 235: ffi 5 (Brown 1994), corresponding
to 1998 November 18.0, the observed fireball flux peaked
much earlier at – fi = 234: ffi 5 (1998 November 17.1).
The observed fireball outburst was distinguished by an
exceptionally low population index (Arlt 1998), i.e. by a
predominance of very bright meteors originating from large
dust grains with sizes ranging up to a few centimetres. The
highest level of fireball activity lasted approximately half
a day, indicating the presence of a narrow, concentrated
substream containing relatively large particles. The different
particle size distribution together with the surprising differ­
ence in time from the predicted shower maximum suggests
that the outburst was produced by a distinct population
of large grains moving in a different orbit from that of the
parent comet.
2 RESONANT MOTION
A substantial number of short­period comets exhibit
resonant motion (Marsden 1970; Franklin et al. 1975;
Emel'yanenko 1987; Carusi & Valsecchi 1987). The impor­
tance of resonances has been demonstrated in the long­term
dynamical evolution of both Encke­type orbits (Asher &
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2 D.J. Asher, M.E. Bailey & V.V. Emel'yanenko
Figure 1. Evolution in semi­major axis a of 55P/Tempel­Tuttle for 1500 years (solid line), together with that of a typical particle
ejected in 1333 (dotted line) that intersects the Earth at 1998 November 17.1. The critical argument, oe, plotted for the 5/14 mean­
motion resonance with Jupiter, is a measure of the location of the particle with respect to the resonance centre. The comet appears to
have entered the resonance during the seventh century, indicated by the transition of oe from circulating to librating values.
Clube 1993; Farinella et al. 1994; Valsecchi et al. 1995)
and Halley­type comets (Asher et al. 1994; Bailey &
Emel'yanenko 1996). Indeed, recent work (e.g. Bailey 1996)
has emphasized some surprising similarities in the long­
term orbital evolution of these otherwise rather different
classes of orbit. So far as the Leonids are concerned, Comet
55P/Tempel­Tuttle is well known to be in the 5/14 mean­
motion resonance with Jupiter (Stoney & Downing 1899).
We therefore considered the possibility that dust particles
released from the comet at a previous perihelion passage
might be trapped in the same resonance, leading to a high
particle concentration in space and also to a sufficiently dif­
ferent orbit to explain the observed meteor outburst.
If a Leonid particle lies in the j=j 0 = 5=14 mean­motion
resonance with Jupiter, it will have a mean semi­major axis
a ' 10:35 au (Emel'yanenko 1988). Jovian perturbations
constrain the particle's semi­major axis a to vary periodi­
cally, with corresponding variations in the critical argument
oe = j 0 M \Gamma j(MJ +!J
+\Omega J \Gamma !
\Gamma\Omega\Gamma1 where M , !
and\Omega are
the mean anomaly, argument of perihelion and longitude of
ascending node respectively, the suffix J denoting Jupiter.
The motion is analogous to that of a simple pendulum, the
period and amplitude depending on the particle's distance
from the resonance centre, oe. Fig. 1 shows the evolution
of (a; oe) for 55P/Tempel­Tuttle for approximately the last
1500 years.
The large dust grains ejected from the comet are pre­
dominantly ejected into the same 5/14 resonance as the
comet, and cannot spread around the orbit in the usual
way. (Other resonances, such as the 1/3 and 4/11, may
also be populated, but these do not lead to an outburst
in 1998.) Instead, they produce a long­lived, high­density
concentration of particles, taking the form of an arc of ma­
terial located close to, but not necessarily identical with,
the parent cometary orbit. The `regular' motion of librat­
ing particles within the resonance contrasts with the more
chaotic motion of non­resonant grains, and allows the local
particle density to build up to a level comparable to that of
the non­resonant, recently ejected particles. These features
of resonant meteoroid streams have been investigated pre­
viously, both numerically and analytically (Emel'yanenko
1984, 1988). Resonant particles, despite their age, may pro­
duce very concentrated meteoroid streams (Emel'yanenko &
Bailey 1996), which although potentially dangerous are for­
tunately predictable. Indeed, with the benefit of hindsight,
the a priori probability of a fireball outburst was higher in
1998 because the Earth passed close to the centre of the res­
onant zone occupied by 55P/Tempel­Tuttle and much of its
debris.
Resonances have similarly been proposed as relating
to meteor displays and meteoroid bombardment from other
streams, such as the Lyrids (Emel'yanenko 1991), Taurids
(Asher & Clube 1993; Asher & Izumi 1998) and Perseids
(Jenniskens et al. 1998). The orbit of the Lyrid parent comet
is rather uncertain, but the effects of a resonance are sug­
gested by the detailed variation of the meteor shower from
year to year and the location of the showers with respect to
the predicted centre of the resonance. For the 1998 Leonids,
however, the well known cometary orbit together with the
regular rather than stochastic nature of the resonant orbits
allow us to prove the resonant motion by identifying the
particular time when the particles were ejected.
For this purpose we used the Radau integrator (Ever­
hart 1985), two orbits for the comet (Nakano 1997, 1998),
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1998 Leonid outburst 3
Figure 2. Distribution in mean anomaly M at 1998 November
17.1 of particles ejected at low velocities (corresponding to an ini­
tial displacement j\Deltaaj ! 0:05au from the semi­major axis of the
comet) at successive perihelion passages from 1001 to 1499. This
shows the strong concentration of 5/14 resonant particles mainly
within a range of ¸10 ffi . If the orbital periods of the particles had
remained at their initial values (i.e. there was no resonance), the
range of M would be much wider, as shown schematically by the
solid line.
and initial planetary elements (Mercury to Neptune) taken
from the JPL ephemeris DE403. The orbits were based on
observational arcs respectively from 1366 to 1997 and from
1866 to 1998, the fact that the results were derivable with ei­
ther representing a useful consistency check. The comet was
integrated backwards in time, using the Mercury integrator
package (Chambers & Migliorini 1997), including its non­
gravitational acceleration, to find its orbit at each previous
perihelion. This indicated that it has been resonant since the
seventh century (Fig. 1). Beginning at each of the past 42
perihelion passages, 40 particles were integrated forward to
1998 November 17.1, checking also the possible contributions
to the Leonid shower at other dates including 1965, 1966,
1999, and 2000. These particles were assumed to be ejected
at perihelion, varying only the semi­major axis a since that
is what dominates the subsequent evolution. The value of a
was initially chosen to be within 0.2 au of the comet, with
particles spaced equally by 0.01 au. The integrations start­
ing more than a few centuries ago showed that particles were
injected into the resonance, and usually remained in it until
the present time, although only over a relatively small range
¸0.05 au of initial semi­major axis. (Occasionally, when the
comet was itself near the centre of the resonance, this range
extended more than 0.1 au.)
The amplitudes of oscillation about the resonance cen­
tre vary among the different particles, but the overall effect
is that they concentrate mainly over a range of ¸10 ffi in mean
anomaly M (Fig. 2). If, for each ejection epoch, the spread
in M were to increase linearly with time (which it would
if all orbital periods remained constant, and which it does
for the first century or so), the range in M in Fig. 2 would
be of order 90 ffi . At present, the comet is located near the
leading edge of the resonant concentration, while the Earth
passed through the concentration a little behind the centre
in November 1998.
We next explored the spatial structure of this resonant
substream with regard to identifying the particles that pro­
duced the observed fireball outburst. In order for particles
ejected at a particular previous perihelion passage to collide
with the Earth in 1998 during their descending nodal pas­
sage at heliocentric distance rD , it is necessary that they
(a) cross the ecliptic at the same heliocentric distance as
the Earth; (b) have orbits such that the
longitude\Omega of their
ascending node corresponds exactly to the time of the out­
burst; and (c) have mean anomalies such that they cross the
descending node at the time of the outburst (1998 November
17.1).
For a century or two, the range in mean anomaly M
of particles ejected at a given time tends to spread out as
a reasonably smooth function of the orbital period at ejec­
tion, equivalently the initial semi­major axis a0 . Thereafter,
M as a function of a0 becomes increasingly fragmented over
the range \Sigma0.2 au in a0 being considered, but our chosen
resolution of 0.01 au in a0 nevertheless allows most ranges
in a0 , at most perihelion passages, to be excluded as possi­
ble sources of meteors in 1998, i.e. condition (c) is certainly
not satisfied. As regards condition (a), rD (in 1998) varies
as a function of a0 through planetary perturbations, but, as
with (c), there is sufficient pattern in rD for most ranges
of a0 to be excluded. Here we required rD to be within a
few times 0.0001 au of the Earth's value, permitting such
dispersion on account of variations in orbital elements other
than a that may occur on ejection (cf. Asher 1999). For
resonant particles, the further dispersion in rD over several
centuries is significantly limited by the effects of the reso­
nance (Emel'yanenko & Bailey 1996).
Over most of the chosen ranges of a0 no meteoroids
could collide with the Earth in 1998 because conditions (a)
and/or (c) were not satisfied. Repeating the integrations
with a finer grid of a0 ­values, in steps of 0.0005 au, over
all limited ranges of initial semi­major axis where the pre­
liminary integrations suggested that conditions (a) and (c)
might jointly apply, we found one particular set of particles,
namely a subset of those released at the perihelion passage
of 1333, which could collide with the Earth in 1998 (Fig. 3).
This set of particles was unique in the range of a0 over which
both rD and \Deltat (Fig. 3) were close to the required values.
For example, a subset of the particles released in 1433 (not
shown in Fig. 3) apparently allowed Earth collisions in 1998,
but only if a0 was extremely finely tuned to take its ap­
propriate value. This would mean that the resultant spatial
density of particles in 1998 was substantially lower than for
the 1333 particles.
Having identified, from conditions (a) and (c) alone,
1333 as the perihelion passage with the dominant contribu­
tion to the 1998 fireball flux, we can check condition (b) for
those specific particles. The nearly regular nature of these
resonant orbits means
that\Omega is now rather precisely spec­
ified, in contrast to the situation for chaotic orbits when
after some time there is considerable dispersion in the (rD ,
\Omega\Gamma plane (Emel'yanenko & Bailey 1996). Based on our inte­
grations, a fireball outburst due to resonant particles would
be predicted around – fi ' 234: ffi 5 (Fig. 3), an outstanding
match to the observed value and all the more impressive
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4 D.J. Asher, M.E. Bailey & V.V. Emel'yanenko
Figure 3. Orbital properties at 1998 November 17.1 of parti­
cles released at perihelion in September 1333, versus initial semi­
major axis a 0 . The figure shows (a) the heliocentricdistance of the
descending node r D (au) together with the heliocentric distance
of the Earth r \Phi (dotted line); (b) the longitude of the ascending
node \Omega\Gamma the dotted line corresponding to the solar longitude of the
observed outburst (1998 November 17.1); and (c) the difference
in time \Deltat (days) of the particles' nodal crossing from the time
of the observed outburst. These results show that the conditions
for meteors to be produced at the observed time are satisfied if
a 0 ' 10:30au.
when noted as being of order a day earlier than passage
through the comet's orbital plane.
3 CONCLUSIONS
We have therefore shown that the particles ejected from
55P/Tempel­Tuttle in 1333 with initial semi­major axes dif­
ferent from that of the comet by \Deltaa ' \Gamma0:024 au could
intersect the Earth exactly at 1998 November 17.1 (Fig. 3).
Such a change in semi­major axis corresponds to ejection of
particles close to perihelion at a transverse velocity around
\Gamma2:4 m s \Gamma1 , i.e. in the direction of motion opposite to the
orbital motion of the comet. (Allowing for the small effects
of radiation pressure on typical fireball­producing particles,
this velocity increases to ¸ \Gamma4 m s \Gamma1 .) Our results also show
a probable additional contribution by large particles ejected
in 1433, intersecting the Earth two hours later, but involving
significantly fewer particles than from the 1333 perihelion
passage.
As to future events, the concentration of resonating par­
ticles, including the comet, has been carried along on its
orbit and is now well past the Earth. The strong Leonid
activity expected to occur in 1999 close to – fi ' 235: ffi 3 (cor­
responding to 1999 November 18.1), and in 2000 close to
– fi ' 236: ffi 3 (2000 November 18.3), will be primarily due to
meteoroids ejected from the comet in 1932, 1899 and 1866
(Brown & Jones 1996; Wu & Williams 1996; Yeomans et
al. 1996; Kondrat'eva, Murav'eva & Reznikov 1997; Asher
1999). These particles are densely concentrated in space be­
cause they have had relatively little time since ejection to
disperse. We predict that the population index of the 1999
Leonid shower should correspond to a normal population
of fireballs. In contrast, the 1998 fireball outburst was due
to meteoroids which were (a) generally larger, and so more
likely to be injected into orbits nearer the comet (i.e. into
resonant orbits), and (b) concentrated in space many cen­
turies after ejection owing to the dynamical properties of
the resonance. The 1998 fireballs were thus an impressive
observational demonstration of one of the most important
dynamical features of meteoroid streams in Halley­type or­
bits.
ACKNOWLEDGMENTS
We thank John Chambers, Victor Clube, Brian Marsden and
Iwan Williams for helpful comments, and John Chambers for
the use of his Mercury integrator package. This work was
supported by DENI, PPARC and RFBR.
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