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Dynamics of Leonid dust trails (the cause of storms)
D.J. Asher
Armagh Observatory, Northern Ireland
(Last revised 2000 February 7)
Although the background level of meteors from the Leonid stream is not
especially high, within the stream are dense, narrow trails of meteoroids and
dust, the debris of Comet 55P/Tempel-Tuttle. These trails are similar to those
discovered by the Infra-Red Astronomical Satellite in the orbits of other peri-
odic comets. When the Earth encounters a trail, a meteor outburst or storm
occurs. Two qualitatively dierent kinds of trail are present in the Leonid
stream. `Normal' trails, up to a few centuries old, form simply because me-
teoroid particles of slightly smaller and larger orbital periods than the comet
gradually stretch ahead of and behind the comet. The number density of par-
ticles is much higher at the centre of these trails than elsewhere in the Leonid
stream. Therefore the Earth's passages close to the centre of these trails are
associated with the highest Zenithal Hourly Rate storms. Trails of the second
kind form as a result of resonant dynamical behaviour over more than a few
centuries. Although the overall number densities of meteoroid particles in reso-
nant trails are smaller than in normal trails, the resonant trails are rich in larger
particles. This meant that the 1998 outburst had much lower ZHR than the
greatest Leonid storms, but was rich in reballs. The positions of both kinds
of trail in space can be accurately calculated, by accounting for gravitational
perturbations, allowing meteor storms to be predicted.
1 DYNAMICS OF YOUNG DUST TRAILS
Trail formation
Each time an active, periodic comet such as 55P/Tempel-Tuttle returns to peri-
helion, ices near the surface of the cometary nucleus sublimate, and the expanding gas
drags small, solid particles (meteoroids and dust) away from the nucleus. The smallest
particles are quickly swept into the comet's dust tail by solar radiation pressure. Some-
what larger meteoroid particles, of a size capable of producing visual meteors (1 mm
grains will give visual Leonids) are also acted on by radiation pressure (see below) but to
a lesser degree. After being released from the nucleus, these particles are able to remain
within the Leonid stream, which is basically a tube of meteoroidal material surrounding
the comet orbit. The particles are not immediately scattered at random throughout the
stream, and it is the structure within the stream, i.e., the existence of regions of higher
and lower density, that causes variations in meteor activity.
As they escape from the cometary nucleus, the meteoroids possess some velocity,
relative to the nucleus. This ejection velocity is probably of order tens of m s 1 for
mm-sized particles, compared to 42km s 1 (at perihelion) for 55P/Tempel-Tuttle's
orbital velocity around the Sun. This small dierence in velocity means that each me-
teoroid's orbit is similar but not identical to the comet's orbit. Immediately after ejec-
tion, therefore, particles' orbits cover a range of orbital periods, concentrating towards
55P/Tempel-Tuttle's period of 33 yr. It is a simple consequence of orbital motion that
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Figure 1. Evolution of a Leonid dust trail, shown after 1, 2, 3 and 4 revolutions, neglecting
radiation pressure and gravitational perturbations. The x-axis is the time by which particles lead
or follow the comet. In this representation, particle density in the trail is inversely proportional
to spacing between lines. Two points to note are:
(i) At any one time, the density prole along the trail shows a concentration close to the
comet. The extent of this concentration could be adjusted (compressed or expanded) depending
on the assumed model of ejection from the comet nucleus (in general, smaller ejection velocities
give a smaller range of meteoroids' orbital periods, and compress the concentration towards the
comet more), but here is in reasonable accord with expected ejection velocities for particles in
a Leonid trail that would produce visual meteors.
(ii) The density becomes diluted with time, since the separation between particles increases
(any particle with a longer orbital period gets progressively further behind a particle whose
period is shorter). In this approximation of no gravitational perturbations, the trail necessarily
lengthens at a constant rate.
particles with smaller and larger periods will progressively get ahead and fall behind
respectively. The result is elongation into a trail , whose length increases with time as
particles stretch further ahead and behind (Fig. 1).
Solar radiation falling on meteoroid particles exerts a force on them. Radiation
pressure varies inversely with the square of the distance from the Sun, as does Newtonian
gravity, but acting in the opposite direction. Any given particle therefore orbits the Sun
on an ellipse, as it would if subject to solar gravity alone, but with the inverse square
force reduced by a constant fraction. Eectively, the Sun pulls the particle around its
orbit less strongly, and so an orbital revolution takes longer to complete. This means
that dust trails tend to be shifted backwards relative to the comet. The size of the
radiation pressure force varies with the sizes and densities of particles, being greater,
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Figure 2. Evolution of a Leonid dust trail, shown after 1, 2, 3 and 4 revolutions, neglecting
gravitational perturbations, but allowing for radiation pressure at a suitable average value for
particles that produce visual meteors. Cf. Fig. 1.
as a fraction of solar gravity, for smaller particles. The eect on a dust trail for a
single value of the radiation pressure parameter, that can reasonably be expected to
correspond to visual meteors, is illustrated in Fig. 2.
The above discussion was of the density prole along a trail. Evidently the density
also varies across the trail. Expected ejection velocities, based on current knowledge
of meteoroid ejection processes from comets, imply that mm-sized particles in a trail
are contained within a cross section whose width is of order ten Earth diameters at
1 astronomical unit from the Sun. Moreover, as intuitively expected, the density prole
increases sharply towards the nominal centre of the trail. Radiation pressure increases
the cross section, but not substantially for these particles. As this cross section is very
narrow on the scale of the whole Leonid stream, the chance of the Earth encountering
the core of any one trail, on a random passage through the stream, is quite small. But
dynamical calculations can make such statements about particular trails denite, rather
than based on chance.
Evolution under planetary perturbations
Dust trails evolve through the gravitational perturbations of the planets. One con-
sequence is that the rate of lengthening (cf. point (ii) in Fig. 1 caption) is dierent at
dierent points along a trail. This eect can be accurately evaluated using a computer
program that takes account of the planets. In practice, for the rst couple of revolutions,
the density prole along a trail evolves as shown schematically in Figs 1 & 2, gradually
starting to deviate thereafter.
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However, the most important eect of planetary perturbations is that they can shift
the orbits of dust trail particles towards or away from the Earth's orbit. As these shifts
are often by distances much greater than a trail's width, they can make the dierence
between having a spectacular meteor storm, or no outburst at all.
Even after less than one revolution, trails are long enough that perturbations vary
greatly along the trail. For example, one part of a trail may at some time be signicantly
nearer Jupiter than another, and therefore get shifted signicantly more by the planet's
gravity than the part of the trail that is further away. The other side of this argument
is that particles a similar distance along a single trail, i.e., that are approximately
comoving, undergo the same perturbations, and so do not disperse relative to each
other. Thus all the particles in one part of a trail can be shifted to bring them nearer
to or further from the Earth's orbit, but they do not shift relative to each other, and
the trail's cross section at any one point does not become wider with each successive
revolution (dynamical simulations show this to be true for a few centuries).
Just as they shift particle orbits, perturbations continuously shift the comet's orbit,
and the comet returns to a slightly dierent point at each successive perihelion. This
means that each new dust trail, arising from the material released during one perihelion
return, begins in a slightly dierent position from previous trails. Additionally, the
conguration of the planets changes every 33 yr. It follows that every trail's dynamical
evolution is unique, and must be calculated individually, using the computer program
that evaluates planetary perturbations. It is also clear that separated trails, generated at
33 yr intervals, do indeed exist, rather than all trails coinciding around a single orbit.
The dust trail structure of the stream may be thought of as multiple, dense, narrow
strands, owing through the Leonid stream as a whole, diverging from the comet both
in front, and (mostly) behind. No trail lies exactly along an elliptical orbit.
Ecliptic crossings
As perturbations vary along a trail, they must be calculated for the parts of each
trail that are of interest. For the purpose of predicting meteor activity, the relevant
parts of the trails are those that pass through the plane of the Earth's orbit, from north
to south, in mid-November of each year. Fig. 2 shows that a trail can soon lengthen
suфciently that the front is some years ahead of the back, and successive sections (of
reasonable density) of the same trail can reach the ecliptic in quite a few consecutive
mid-Novembers. A computer program can be used to calculate the dynamical evolution
of these parts of trails, from the time when particles are released from the comet until
the time (mid-November of some year) when they reach the ecliptic, and to specify the
point where each trail section crosses the ecliptic. The closeness of these crossing points
to the Earth's orbit determines whether and at what intensity meteor storms occur. If
there is a storm, it occurs at the time when the Earth reaches the part of its own orbit
that is nearest to the crossing point.
As an example, Fig. 3 is the situation in 1966, showing the places where trails cross
through the ecliptic. Leonid orbits projected on to the ecliptic would be nearly parallel
to the Earth's orbit in this region (with Leonid particles travelling in the opposite
direction to the Earth), but the orbital planes of Leonids and Earth are inclined to
each other by 18 ф . In Fig. 3, trail cross sections are idealised as ellipses, avoiding
unnecessarily detailed discussion of the exact density prole. It is seen that the most
spectacular meteor display of the 20th century occurred when the Earth passed near
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Figure 3. Cross sections of dust trails that passed through the ecliptic in 1966 November. Trails
that were 1 to 6 revolutions old are plotted, labelled by the year in which they were generated
(from 1932 back to 1767). The Earth's orbit is shown, and the Earth's position, exaggerating
its physical size 10 times, at dates (Universal Time) in 1966. A cross indicates where the comet
crossed the ecliptic in 1965, and does not represent a dust trail; although an incipient trail is
present in 1965 (due to material being released at that perihelion passage), it does not extend
far from the comet and is not present in 1966 November.
the centre of the 1899 trail, which was then 2 revolutions old.
The occurrence and timing of storms has been described as a `predictable lottery'.
It is a lottery in the sense that gravitational perturbations can shift dense dust trails
away from the Earth's orbit, depriving the Earth of a meteor storm, or vice versa. But
it is predictable because the perturbations can be accurately calculated.
2 RESONANT TRAILS
The 1998 outburst
The positions of young dust trails in 1998 are plotted in Fig. 4. No encounter of the
Earth with a trail is evident. However, a second kind of trail is present in the Leonids
(and other streams).
The dynamics of Leonid particles is ultimately chaotic, generally on timescales of a
few centuries. Meteoroids that come close to the Earth during some perihelion passage
(without actually impacting) are signicantly de ected by the Earth's gravity. The
gravitational eect can be enough to scatter them into the background Leonid stream,
and so a (short) subsection of a trail that comes near the Earth is lost from the trail.
Gradually, more of each trail is lost. A trail can survive as a narrow, coherent struc-
ture for a dozen revolutions or so, meaning that this number of `normal' trails exist
simultaneously, one for each of the comet's last dozen perihelion passages. Beyond
this timescale, so much of a trail has been fragmented or scattered that it is no longer
appropriate to regard it as a trail.
There is, however, a dynamical mechanism that can inhibit this chaotic scatter-
ing. Comet 55P/Tempel-Tuttle makes 5 revolutions of the Sun for every 14 of Jupiter.
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Figure 4. Cross sections of dust trails that passed through the ecliptic in 1998 November. The
comet reached the point shown in 1998 March. The section of the 1899 trail that supposedly
had the correct orbital period to bring it to the ecliptic in 1998 November had its evolution
disrupted because of a fairly close approach to Earth in 1965.
The comet does not merely happen to have an orbital period that is in the region of
14/5 times Jupiter's; instead it turns out that the gravity of Jupiter, the most mass-
ive perturbing planet, acts systematically on the comet, imposing this 5 to 14 pattern
on the comet's orbital period. The comet is said to be in the 5 to 14 resonance with
Jupiter. Although the comet's period may be slightly below the resonant value during
one revolution, and slightly above during another, Jupiter keeps forcing the comet back
to the 5 to 14 pattern in the average timing of the comet's returns. Such a resonant
state can persist for many thousands of years, and the best estimate at present is that
55P/Tempel-Tuttle entered the 5:14 resonance in the 7th century.
In the absence of resonances, particles in normal dust trails (Sec. 1) would all be
chaotically scattered into the Leonid background, with much of each trail having dis-
appeared after a dozen revolutions. However, detailed dynamical studies [1], beyond
demonstrating that 55P/Tempel-Tuttle and other orbits can be resonant, also reveal
that (i) resonances can restrict particles to lie on quite narrow arcs over long timescales,
rather than chaotic scattering into a wide region occurring; and (ii) the orbital evolu-
tion of particles in those arcs generally has a much higher degree of predictability, unlike
with chaotic behaviour. Computer programs that evaluate planetary perturbations (cf.
Sec. 1) can therefore determine this evolution.
Any such arc of resonant particles develops from a small subsection, comparatively
close to the comet, of one of the `normal', younger trails. However, the resonant dyn-
amics, over timescales of more than a few centuries, is qualitatively dierent from the
dynamics controlling the normal trails. The resonant arcs therefore constitute a second
kind of trail. But as with the normal trails, if the Earth runs through a resonant trail,
a meteor outburst occurs. It was found [2] that a resonant trail consisting of a subset of
the meteoroids released from 55P/Tempel-Tuttle in 1333 gave an excellent match to the
peak time of the 1998 Leonid reball outburst, with secondary components, including a
resonant trail from 1433, contributing to the outburst's overall duration of many hours.
Resonances exist in the asteroid belt, in satellite systems and elsewhere in the solar
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Figure 5. Cross sections of dust trails that passed through the ecliptic in 1999 November.
system. The 1998 Leonid reball outburst was an observational demonstration that
they exist in meteor streams.
Presence of reball-producing particles
Because 55P/Tempel-Tuttle itself is resonant, and resonant orbits are dened by
their orbital period, resonant particles are essentially those orbiting with periods most
similar to the comet. In Figs 1 & 2, these are particles that do not quickly drift away
from the comet's position, since it is the dierence in period that causes particles to get
behind or ahead. Comparision of Figs 1 & 2 shows that when radiation pressure is less
(Fig. 1), i.e., for larger particles, the density peak is closer to the comet's position. In
fact, it is generally expected that larger meteoroids are ejected at lower velocities from
the comet nucleus; this eect would compress the concentration in Fig. 1 still closer to
the comet.
Of course, smaller (usual visual meteor) particles are more numerous than larger
(reball) ones in total. The point is that smaller Leonid meteoroids have less tendency
to occupy resonant regions, whereas a higher proportion of larger ones are inserted into
resonant orbits similar to the comet's. So not only is the timing of the 1998 outburst
predicted, but the preponderance of reballs too.
3 METEOR STORMS 1999{2002
Comet 55P/Tempel-Tuttle, and the resonant zone containing the comet, have moved
on in their orbit, not to return for another thirty years. Only the younger dust trails
(Sec. 1) are relevant for the next few years. Figs 5{8 show the Earth encountering dust
trails in 1999{2002. Various authors [3] independently found essentially the same times
for some or all of the storms and outbursts resulting from these encounters. In Figs
5{8, trails as old as 9 revolutions are plotted (a limit of 6 revolutions was used in Figs
3, 4), and trail cross sections are absent from the plots only if there really is no ecliptic
crossing at the relevant time in November (cf. absence of 1899 trail in 1998, discussed
in Fig. 4 caption).
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Figure 6. Cross sections of dust trails passing through the ecliptic in 2000 November.
Figure 7. Cross sections of dust trails passing through the ecliptic in 2001 November.
A clear pattern is evident in Figs 4{8, where the cross section of any one trail has
a tendency to be further, with each successive year, from the point where the comet
crossed the ecliptic in 1998 March. That is, the various trails tend to become more
separated in space, as one progresses further behind the comet, although some bunching
(e.g., the cross sections shown for the 1800 and 1833 trails are quite close together) can
occur. In terms of the probabilistic description of trail encounters, this corresponds to
trail cross sections being randomly distributed over a wider region when one is further
behind the comet, but as has been discussed, the random element is entirely removed
by precise calculations of planetary perturbations.
The main purpose of this article has been to describe the structure within the Leonid
stream, and to explain the dynamics of why trails are formed and how they evolve. The
accuracy with which dust trail calculations can actually predict meteor storms in prac-
tice is discussed elsewhere [4]. A method to put the discussion of density proles along
and across trails (Sec. 1) on to a quantitative basis [5] implies that the highest ZHR
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Figure 8. Cross sections of dust trails passing through the ecliptic in 2002 November.
Leonid storms of the present few years will occur in 2001 and 2002 (the former year
having the advantage of new moon), when the Earth goes near the centres of various
trails (Figs 7, 8). The increased distance from the centre of the 1899 trail in 1999
(Fig. 5) as compared to 1966 (Fig. 3) led to the ZHR being much less than in 1966. But
as everyone at the 1999 Jordanian Leonid Meteors Conference knows, even the 1999
storm was quite something.
REFERENCES
[1] For example, see V.V. Emel'yanenko & M.E. Bailey, 1996, in ASP Conf. Ser. Vol. 104,
Physics, Chemistry and Dynamics of Interplanetary Dust, eds B.  A.S. Gustafson & M.S.
Hanner, Astron. Soc. Pac., San Francisco, pp. 121{124, and other references given therein
[2] D.J. Asher, M.E. Bailey & V.V. Emel'yanenko, Mon. Not. R. Astron. Soc., 304, L53{L56,
1999, and Irish Astron. J., 26, 91{93, 1999
[3] E.D. Kondrat'eva & E.A. Reznikov, Sol. Syst. Res., 19, 96{101, 1985; E.D. Kondrat'eva, I.N.
Murav'eva & E.A. Reznikov, Sol. Syst. Res., 31, 489{492, 1997; D.J. Asher, Mon. Not. R.
Astron. Soc., 307, 919{924, 1999; R.H. McNaught & D.J. Asher, WGN, 27, 85{102, 1999,
updated on IMO-News (see http://www.arm.ac.uk/leonid/last1999.html); E. Lyytinen,
Meta Res. Bull., 8, 33{40, 1999
[4] R.H. McNaught, The Astronomer, 35, 279{283, 1999
[5] McNaught & Asher (ibid.)
Helpful comments from Robert H. McNaught led to signicant improvements in
the text. The article is based on my presentation at the 1999 Jordanian Leonid
Meteors Conference. It is a pleasure to thank the Jordanian Astronomical
Society for organising such a successful and enjoyable meeting.
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