acceleration arising between the nucleus and a particle as it slows drifts away. With
Monte Carlo techniques it is, of course, straightforward to initialise particle velocities within limits. Sunward ejection within a 30
half-angle cone would be a
reasonable starting point, for example, at velocities slightly higher than the escape
velocity. The particles can then be tracked through time. The influence of radiation
pressure can also be included through the β parameter (Eq. 4.72). Two example
results for two different values of β are shown in Fig. 4.60. The test case shown here
is rather generic—a Jupiter family comet with a perihelion at 1.3 AU with emission
of particles in a 30
cone about the sub-solar point at a velocity of 6 m s
À1 relative to
the nucleus. The plots show distributions after 1.6 orbits of the comet about the Sun
with t ¼ 0 at aphelion. In the top panels, we can see the distribution of particles when
looking down upon the orbital plane of the comet and the influence of β is clearly
evident. In the centre panels, the viewing direction is in the orbital plane of the comet
from the direction of the Sun. The particles are seen to be distributed about the orbital
plane independent of β although the structure of the distribution shows dependence
upon β. Note that particles can appear on both sides of the nucleus depending upon
viewing geometry and the value of β. As discussed by Fulle and Sedmak (1988), the
photometric analysis of these structures can provide information on large
(millimetre-sized) particles ejected by nuclei. However, there are numerous free
parameters in the modelling including the distribution of β values, the assumed
surface emission distribution, and its time dependence.
The neck-line structures are seen in the vicinity of the nucleus itself and are,
relatively speaking, quite young. However, the trajectories of these large particles
will evolve and, with time, spread out further to produce a cloud of particles along
the orbital path. These older particles can be detected in the infrared through their
thermal emission and are referred to as cometary dust trails. The significance became
clear when observations were made by the IRAS spacecraft (Eaton et al. 1984; Sykes
et al. 1986) and it was recognized that these trails were consistent with low velocity
emission over timescales of many years and possibly decades.
Spitzer observations were acquired of many dust trails associated with known
comets. Two examples can be seen in Fig. 4.61. The upper panel shows 2P/Encke
(Kelley 2006). The white lines indicate the cometary dust trail. The lower panel
shows a similar observation for 67P (see Kelley et al. 2008). Here the dust trail is far
less bright particularly to the left of the nucleus in the image. The orbit of 67P was
perturbed by a close approach to Jupiter in 1959 and hence we may be seeing here a
reduced dust trail brightness purely because 67P has not been in its present orbit for
more than a few orbital periods. The particles in the trails are themselves subject to
perturbations and hence orbital stability over long timescales is not always assured.
Dust trails are effectively meteor streams and if they intersect the Earth then this
can result in a meteor shower. When (3200) Phaethon was discovered (Davies et al.
1984), it was recognized as being the probable parent of the Geminid meteor stream
(Williams and Wu 1993) and on that basis it was proposed as being a “dead” comet
meaning that it had been active once but had ceased being active as a result of either
volatile loss or an activity choking mechanism. The stream itself has been estimated
as being about 1000 years old. While this link hinted at Phaethon’s unusual
372
4 Dust Emission from the Surface
Monte Carlo techniques it is, of course, straightforward to initialise particle velocities within limits. Sunward ejection within a 30
half-angle cone would be a
reasonable starting point, for example, at velocities slightly higher than the escape
velocity. The particles can then be tracked through time. The influence of radiation
pressure can also be included through the β parameter (Eq. 4.72). Two example
results for two different values of β are shown in Fig. 4.60. The test case shown here
is rather generic—a Jupiter family comet with a perihelion at 1.3 AU with emission
of particles in a 30
cone about the sub-solar point at a velocity of 6 m s
À1 relative to
the nucleus. The plots show distributions after 1.6 orbits of the comet about the Sun
with t ¼ 0 at aphelion. In the top panels, we can see the distribution of particles when
looking down upon the orbital plane of the comet and the influence of β is clearly
evident. In the centre panels, the viewing direction is in the orbital plane of the comet
from the direction of the Sun. The particles are seen to be distributed about the orbital
plane independent of β although the structure of the distribution shows dependence
upon β. Note that particles can appear on both sides of the nucleus depending upon
viewing geometry and the value of β. As discussed by Fulle and Sedmak (1988), the
photometric analysis of these structures can provide information on large
(millimetre-sized) particles ejected by nuclei. However, there are numerous free
parameters in the modelling including the distribution of β values, the assumed
surface emission distribution, and its time dependence.
The neck-line structures are seen in the vicinity of the nucleus itself and are,
relatively speaking, quite young. However, the trajectories of these large particles
will evolve and, with time, spread out further to produce a cloud of particles along
the orbital path. These older particles can be detected in the infrared through their
thermal emission and are referred to as cometary dust trails. The significance became
clear when observations were made by the IRAS spacecraft (Eaton et al. 1984; Sykes
et al. 1986) and it was recognized that these trails were consistent with low velocity
emission over timescales of many years and possibly decades.
Spitzer observations were acquired of many dust trails associated with known
comets. Two examples can be seen in Fig. 4.61. The upper panel shows 2P/Encke
(Kelley 2006). The white lines indicate the cometary dust trail. The lower panel
shows a similar observation for 67P (see Kelley et al. 2008). Here the dust trail is far
less bright particularly to the left of the nucleus in the image. The orbit of 67P was
perturbed by a close approach to Jupiter in 1959 and hence we may be seeing here a
reduced dust trail brightness purely because 67P has not been in its present orbit for
more than a few orbital periods. The particles in the trails are themselves subject to
perturbations and hence orbital stability over long timescales is not always assured.
Dust trails are effectively meteor streams and if they intersect the Earth then this
can result in a meteor shower. When (3200) Phaethon was discovered (Davies et al.
1984), it was recognized as being the probable parent of the Geminid meteor stream
(Williams and Wu 1993) and on that basis it was proposed as being a “dead” comet
meaning that it had been active once but had ceased being active as a result of either
volatile loss or an activity choking mechanism. The stream itself has been estimated
as being about 1000 years old. While this link hinted at Phaethon’s unusual
372
4 Dust Emission from the Surface