3.4 Gas Expansion
3.4.1 The Initial Conditions
At the beginning of this section, we made four assumptions about the gas distribution. The first three were that there is a point source, that gas emission from the
nucleus is isotropic, and that the gas velocity is constant. Close to the nucleus, none
of these assumptions is valid. Within ten nucleus radii, the nucleus can no longer be
considered a point source. The outgassing is driven by solar insolation and significant inhomogeneity in emission may be superimposed upon this. Finally, the gas
must be accelerated to its final velocity from its initial state at the surface of the
nucleus.
The investigation of the properties of the gas distribution in the immediate
vicinity of the nucleus now forms an important tool in trying to understand the
outgassing properties of the nucleus. The idea is that by understanding the gas
distribution in the innermost gas coma, one can deduce the surface outgassing
distribution and from that derive properties of the nucleus surface.
This appears logical and straightforward but the mathematical tools needed to
address specific questions may change depending upon the flow regime. Figure 3.19
is a schematic diagram of the different flow regimes possible near the source. We
begin by discussing an active comet.
The mean free path is defined as
λ MFP ¼
1
ffiffi ffi
2
p σ col n g
ð3:42Þ
where σ col is the cross-sectional area of the species and n g is the local density. For
water molecules, the collisional cross-section is around 2.5 10
À15 cm
2 (Crovisier
1984). Eq. (3.1) can be substituted for n g in Eq. (3.42) to obtain a mean free path with
cometocentric distance. However, a more realistic value is obtained by assuming a
uniform sphere emitting gas proportional to the cosine of the incidence angle. The
mean free path at the sub-solar point is then given by
λ MFP ¼
πv g r
2
N
ffiffi ffi
2
p
Q g σ col
ð3:43Þ
where Q g is the total gas production rate and v g is the outflow velocity. But this still
overestimates λ MFP in the region where gas acceleration is important. A crude
approximation to v g is given by
v g ¼ v 1 1 À
r N
r
ð3:44Þ
210
3 Gas Emissions Near the Nucleus
3.4.1 The Initial Conditions
At the beginning of this section, we made four assumptions about the gas distribution. The first three were that there is a point source, that gas emission from the
nucleus is isotropic, and that the gas velocity is constant. Close to the nucleus, none
of these assumptions is valid. Within ten nucleus radii, the nucleus can no longer be
considered a point source. The outgassing is driven by solar insolation and significant inhomogeneity in emission may be superimposed upon this. Finally, the gas
must be accelerated to its final velocity from its initial state at the surface of the
nucleus.
The investigation of the properties of the gas distribution in the immediate
vicinity of the nucleus now forms an important tool in trying to understand the
outgassing properties of the nucleus. The idea is that by understanding the gas
distribution in the innermost gas coma, one can deduce the surface outgassing
distribution and from that derive properties of the nucleus surface.
This appears logical and straightforward but the mathematical tools needed to
address specific questions may change depending upon the flow regime. Figure 3.19
is a schematic diagram of the different flow regimes possible near the source. We
begin by discussing an active comet.
The mean free path is defined as
λ MFP ¼
1
ffiffi ffi
2
p σ col n g
ð3:42Þ
where σ col is the cross-sectional area of the species and n g is the local density. For
water molecules, the collisional cross-section is around 2.5 10
À15 cm
2 (Crovisier
1984). Eq. (3.1) can be substituted for n g in Eq. (3.42) to obtain a mean free path with
cometocentric distance. However, a more realistic value is obtained by assuming a
uniform sphere emitting gas proportional to the cosine of the incidence angle. The
mean free path at the sub-solar point is then given by
λ MFP ¼
πv g r
2
N
ffiffi ffi
2
p
Q g σ col
ð3:43Þ
where Q g is the total gas production rate and v g is the outflow velocity. But this still
overestimates λ MFP in the region where gas acceleration is important. A crude
approximation to v g is given by
v g ¼ v 1 1 À
r N
r
ð3:44Þ
210
3 Gas Emissions Near the Nucleus