decoupled quickly so the resulting dust distribution is strongly dependent upon the
particle radius. Streamlines are superposed on the dust speed panels and show that
large particles can return to the nucleus under the influence of gravity to produce
airfall. This verifies that the concept of airfall to produce the smooth surfaces seen in
Ma’at and Ash on 67P is feasible. It is interesting to note that the dust speed of the
re-impacting particles increases as one moves towards the nightside. This is in some
ways obvious—particles have to be thrown out further to get as far as possible into
the nightside hemisphere and thus the impact speed is maximized and approaches the
escape velocity as they experience the gravitational pull for the longest duration. The
plot also shows the non-radial component of the dust outflow at the terminator. Dust
flow is almost parallel to the surface at the terminator for intermediate-sized and
smaller particles. The variation in the drag coefficient should also be noted. The
terminal velocity of the dust is clearly dependent upon the gas production rate but
Marschall (2017) has shown that the dependence is ~1/√a over a large range of
particle sizes and that scaling according to
v a /
ffiffiffiffiffi ffi
Q g
a
r
ð4:101Þ
can be employed for much of the typical parameter space. It should be clear from this
that the dust size distribution at the nucleus is not the same as that in a unit volume at
some point in the coma with the distribution in the coma being skewed towards
larger sizes such that the exponent in the coma, b c , is
b c ¼ b d À 0:5
ð4:102Þ
if b d defines the power law distribution at the surface. McDonnell et al. (1991)
provided a computation for the size distribution at the surface of 1P/Halley based on
semi-empirical dust velocities from Divine (1981) using their observations
(Fig. 4.22). Della Corte et al. (2016) using the GIADA data determined power law
relationships between the mass and velocity of detected particles and noted a phase
angle dependence. Using all particles detected inside 2.5 AU with the phase angle of
<75
(i.e. within the dayside outflow), a least squares fit gives
v a / m
À0:21Æ0:06
d
ð4:103Þ
showing a slightly steeper dependence of velocity on particle size than implied by
Eq. (4.102) assuming density is independent of size over the fairly narrow range of
particle masses sampled by GIADA. However, two low velocity outliers in the
dataset have a very strong influence on the slope of the least squares fit so that this
is not necessarily inconsistent with Eq. (4.102).
It should also be clear from this discussion that the size distribution measured in
the coma will vary with heliocentric distance for large particles because of the
relationship between the efficiency of gas drag and particle size. Given that
4.7 The Influence of Drag on the Equations of Motion for the Dust
333
particle radius. Streamlines are superposed on the dust speed panels and show that
large particles can return to the nucleus under the influence of gravity to produce
airfall. This verifies that the concept of airfall to produce the smooth surfaces seen in
Ma’at and Ash on 67P is feasible. It is interesting to note that the dust speed of the
re-impacting particles increases as one moves towards the nightside. This is in some
ways obvious—particles have to be thrown out further to get as far as possible into
the nightside hemisphere and thus the impact speed is maximized and approaches the
escape velocity as they experience the gravitational pull for the longest duration. The
plot also shows the non-radial component of the dust outflow at the terminator. Dust
flow is almost parallel to the surface at the terminator for intermediate-sized and
smaller particles. The variation in the drag coefficient should also be noted. The
terminal velocity of the dust is clearly dependent upon the gas production rate but
Marschall (2017) has shown that the dependence is ~1/√a over a large range of
particle sizes and that scaling according to
v a /
ffiffiffiffiffi ffi
Q g
a
r
ð4:101Þ
can be employed for much of the typical parameter space. It should be clear from this
that the dust size distribution at the nucleus is not the same as that in a unit volume at
some point in the coma with the distribution in the coma being skewed towards
larger sizes such that the exponent in the coma, b c , is
b c ¼ b d À 0:5
ð4:102Þ
if b d defines the power law distribution at the surface. McDonnell et al. (1991)
provided a computation for the size distribution at the surface of 1P/Halley based on
semi-empirical dust velocities from Divine (1981) using their observations
(Fig. 4.22). Della Corte et al. (2016) using the GIADA data determined power law
relationships between the mass and velocity of detected particles and noted a phase
angle dependence. Using all particles detected inside 2.5 AU with the phase angle of
<75
(i.e. within the dayside outflow), a least squares fit gives
v a / m
À0:21Æ0:06
d
ð4:103Þ
showing a slightly steeper dependence of velocity on particle size than implied by
Eq. (4.102) assuming density is independent of size over the fairly narrow range of
particle masses sampled by GIADA. However, two low velocity outliers in the
dataset have a very strong influence on the slope of the least squares fit so that this
is not necessarily inconsistent with Eq. (4.102).
It should also be clear from this discussion that the size distribution measured in
the coma will vary with heliocentric distance for large particles because of the
relationship between the efficiency of gas drag and particle size. Given that
4.7 The Influence of Drag on the Equations of Motion for the Dust
333