zero. The ejection mechanism may give the particles an initial velocity but, even if
not, the drag force from the gas (Eq. 4.87) accelerates the particles. Hence, the
product of N d b is no longer a constant—we have what is referred to as “a deviation
from 1/r”.
While it is clear that N d b must decrease as one moves away from the nucleus
because of the drag force, it is not the only issue close to the nucleus. This is not
solely of academic interest. Such deviations might also include the signatures of
other processes influencing the dusty-gas outflow which, in turn, may have causes
relating to the properties of emitted material. For example, the acceleration is related
to the particle structure through the drag equation. The initial velocity prior to
acceleration is related to the ejection process itself. Any non-radial component of
the motion also influences the coma brightness distribution and is related to the gas
dynamics directly above the nucleus and its inhomogeneity.
In addition to the breakdown of the force-free radial outflow approximation
because of drag, the point source approximation must also breakdown when close
to the nucleus. How close is “close” in this case is unclear as it depends upon the
shape of the nucleus and the activity distribution but the diameter of the nucleus
would be a reasonable approximation for the length scale. There are also other
effects such as fragmentation, sublimation, and effects on particles from the gravity
of the nucleus that can also produce deviations from 1/r. Viewing and interpreting
the dust column density is one of the few ways of constraining the effectiveness of
each process although it was recognized during analyses of the data from Giotto that
there are difficulties in interpretation because the processes involved are not well
known and natural assumptions lead to significant ambiguity.
We begin to illustrate the problem by showing an example from Rosetta/OSIRIS
observations of 67P. In Fig. 4.44, an example intensity profile from the coma of 67P
is shown. The zero position for the distance is placed at the projected surface of the
nucleus—in this case at the limb. The reflectance from the dust has been multiplied
by the distance from the surface. Force-free radial outflow from a point source would
predict this value to be constant and clearly it is not.
This can easily be explained by the finite dimensions of the source. One can
assume that each position on the object emits dust in a narrow cone which alone
would produce a 1/r function in column density. Multiple cones dotted across the
finite source make up the total emission but, as one approaches the nucleus along a
fixed direction, a decreasing number of cones contribute to the column and hence the
column density decreases relative to a 1/r distribution and we obtain a result similar
to that seen in Fig. 4.44. Boice et al. (2002) used this type of approach for the initial
interpretation of data from Deep Space 1 at 19P/Borrelly, for example, following
ideas presented in Reitsema et al. (1989).
It is also clear from the dust distribution around the comet that the production rate,
Q d , has a strong angular dependence. For the force free approximation, this would be
of no relevance if the nucleus were a point source. Radial profiles would show a 1/r
distribution but the final value of N d b would be dependent on the angular direction
of the profile from the nucleus. However, non-point source geometry, non-radial
4.10 Processes in the Innermost Coma
351
not, the drag force from the gas (Eq. 4.87) accelerates the particles. Hence, the
product of N d b is no longer a constant—we have what is referred to as “a deviation
from 1/r”.
While it is clear that N d b must decrease as one moves away from the nucleus
because of the drag force, it is not the only issue close to the nucleus. This is not
solely of academic interest. Such deviations might also include the signatures of
other processes influencing the dusty-gas outflow which, in turn, may have causes
relating to the properties of emitted material. For example, the acceleration is related
to the particle structure through the drag equation. The initial velocity prior to
acceleration is related to the ejection process itself. Any non-radial component of
the motion also influences the coma brightness distribution and is related to the gas
dynamics directly above the nucleus and its inhomogeneity.
In addition to the breakdown of the force-free radial outflow approximation
because of drag, the point source approximation must also breakdown when close
to the nucleus. How close is “close” in this case is unclear as it depends upon the
shape of the nucleus and the activity distribution but the diameter of the nucleus
would be a reasonable approximation for the length scale. There are also other
effects such as fragmentation, sublimation, and effects on particles from the gravity
of the nucleus that can also produce deviations from 1/r. Viewing and interpreting
the dust column density is one of the few ways of constraining the effectiveness of
each process although it was recognized during analyses of the data from Giotto that
there are difficulties in interpretation because the processes involved are not well
known and natural assumptions lead to significant ambiguity.
We begin to illustrate the problem by showing an example from Rosetta/OSIRIS
observations of 67P. In Fig. 4.44, an example intensity profile from the coma of 67P
is shown. The zero position for the distance is placed at the projected surface of the
nucleus—in this case at the limb. The reflectance from the dust has been multiplied
by the distance from the surface. Force-free radial outflow from a point source would
predict this value to be constant and clearly it is not.
This can easily be explained by the finite dimensions of the source. One can
assume that each position on the object emits dust in a narrow cone which alone
would produce a 1/r function in column density. Multiple cones dotted across the
finite source make up the total emission but, as one approaches the nucleus along a
fixed direction, a decreasing number of cones contribute to the column and hence the
column density decreases relative to a 1/r distribution and we obtain a result similar
to that seen in Fig. 4.44. Boice et al. (2002) used this type of approach for the initial
interpretation of data from Deep Space 1 at 19P/Borrelly, for example, following
ideas presented in Reitsema et al. (1989).
It is also clear from the dust distribution around the comet that the production rate,
Q d , has a strong angular dependence. For the force free approximation, this would be
of no relevance if the nucleus were a point source. Radial profiles would show a 1/r
distribution but the final value of N d b would be dependent on the angular direction
of the profile from the nucleus. However, non-point source geometry, non-radial
4.10 Processes in the Innermost Coma
351