1P/Halley was very active at the time of the Giotto encounter, other comets with a
similar size distribution at the surface may appear relatively depleted in these large
particles when their inner comae are investigated. Hence, Eq. 4.102 will not hold for
particle sizes close to the tail of the distribution.
Finally, in the acceleration region close to the nucleus (within the first 10–12 km),
where small particles are being accelerated to higher velocities than larger particles,
it is apparent that there will be a rapid change in the size distribution as the
cometocentric distance increases.
4.7.3 Gas-Dust Energy Exchange within the Coma
The dust in the inner coma can influence the radiation field close to the nucleus and
the gas flow. However, the dust density and distribution close to the nucleus varies
with heliocentric distance, position, and level of activity. It should be apparent that
when there is very little dust emission, the influence on the gas flow and the radiation
field is negligible. But when does it become important?
A useful approach here is to use the dust optical depth, τ d , as a proxy. The optical
depth through a part of the dust coma was given in Eq. (4.46). If the brightness of the
dust close to the limb is much smaller than the brightness of the nucleus, then this
indicates that the optical depth must be small. We assume here that the scattering
properties of the dust are similar to those of the nucleus itself. This is clearly not true,
particularly if the particle size distribution is dominated by particles close to the
wavelength of the observation, but this at least allows us to assess when more
detailed calculations might be needed. For the case of 67P, we have seen that
τ d < 0.1 in almost all cases and in images close to perihelion (Fig. 4.17), τ d is
typically 0.05. If the gas velocity is much greater than the dust velocity, this suggests
that, in this case, <5% of gas molecules have momentum exchange with the dust and
hence the gas flow field is only marginally affected by the presence of dust.
This conclusion is a huge simplification and one that has usually been made for
67P even well before the Rosetta rendezvous (see, for example, Tenishev et al.
2011). Without this simplification, the back reaction on the gas arising from the dust
must be calculated which results in an iterative procedure for DSMC calculations or
the treatment of dust as an additional fluid in the Navier-Stokes approach (Rodionov
et al. 2002). The consequences of high dust density are fairly clear. Primarily, the
mass loading of the gas flow results in a slowing of the flow. In addition, the
collisions should result in a more homogeneous coma and an increased gas velocity
component parallel to the surface.
For comets such as 1P/Halley near perihelion, the effects of dust on the gas
probably need to be accounted for. The dust reflectance above the limb can be seen
in Fig. 2.20 and shows it to be comparable to the reflectance of the nucleus itself and
thus τ d % 1. Other calculations based on integrating the results from several Giotto
experiments suggested that τ d % 0.4 (Thomas and Keller 1991) although there are
grounds to believe that the value may have been higher because of inaccuracies.
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4 Dust Emission from the Surface
similar size distribution at the surface may appear relatively depleted in these large
particles when their inner comae are investigated. Hence, Eq. 4.102 will not hold for
particle sizes close to the tail of the distribution.
Finally, in the acceleration region close to the nucleus (within the first 10–12 km),
where small particles are being accelerated to higher velocities than larger particles,
it is apparent that there will be a rapid change in the size distribution as the
cometocentric distance increases.
4.7.3 Gas-Dust Energy Exchange within the Coma
The dust in the inner coma can influence the radiation field close to the nucleus and
the gas flow. However, the dust density and distribution close to the nucleus varies
with heliocentric distance, position, and level of activity. It should be apparent that
when there is very little dust emission, the influence on the gas flow and the radiation
field is negligible. But when does it become important?
A useful approach here is to use the dust optical depth, τ d , as a proxy. The optical
depth through a part of the dust coma was given in Eq. (4.46). If the brightness of the
dust close to the limb is much smaller than the brightness of the nucleus, then this
indicates that the optical depth must be small. We assume here that the scattering
properties of the dust are similar to those of the nucleus itself. This is clearly not true,
particularly if the particle size distribution is dominated by particles close to the
wavelength of the observation, but this at least allows us to assess when more
detailed calculations might be needed. For the case of 67P, we have seen that
τ d < 0.1 in almost all cases and in images close to perihelion (Fig. 4.17), τ d is
typically 0.05. If the gas velocity is much greater than the dust velocity, this suggests
that, in this case, <5% of gas molecules have momentum exchange with the dust and
hence the gas flow field is only marginally affected by the presence of dust.
This conclusion is a huge simplification and one that has usually been made for
67P even well before the Rosetta rendezvous (see, for example, Tenishev et al.
2011). Without this simplification, the back reaction on the gas arising from the dust
must be calculated which results in an iterative procedure for DSMC calculations or
the treatment of dust as an additional fluid in the Navier-Stokes approach (Rodionov
et al. 2002). The consequences of high dust density are fairly clear. Primarily, the
mass loading of the gas flow results in a slowing of the flow. In addition, the
collisions should result in a more homogeneous coma and an increased gas velocity
component parallel to the surface.
For comets such as 1P/Halley near perihelion, the effects of dust on the gas
probably need to be accounted for. The dust reflectance above the limb can be seen
in Fig. 2.20 and shows it to be comparable to the reflectance of the nucleus itself and
thus τ d % 1. Other calculations based on integrating the results from several Giotto
experiments suggested that τ d % 0.4 (Thomas and Keller 1991) although there are
grounds to believe that the value may have been higher because of inaccuracies.
334
4 Dust Emission from the Surface