and as γ is different for water and CO 2 , the resulting output ratio of the water flux to
the total flux is around 61% (as seen in the centre of the jet). In the kinetic case, the
outflow flux ratio is controlled by the square-root of the molecular mass and should
nominally show a similar ratio at source but the water molecules can expand more
quickly through the more diffuse CO 2 resulting in a lower mixing ratio at source.
However, what is more important is that, in the wings of the jets (and particularly
close to the surface in the fluid case), the water mixing ratio is appreciably higher. In
other words, the gas is fractionating. This implies that for jet-like outgassing from a
mixed source, the mixing ratios of gas species measured at one point in the
innermost coma may be substantially different from the mixing ratios of the subliming sources.
It should also be pointed out (although it should be apparent from the previous
discussion) that in low production rate cases, inhomogeneous composition can lead
to differing outflow velocities between species and therefore local densities may not
reflect the actual surface composition but be biased towards heavier, slower moving,
molecules.
3.4.5 Examples of Near-Nucleus Gas Flow
3.4.5.1 Cases with Spherical Sources
The observations of cometary nuclei show them to be highly irregular but calculations with spherical symmetry remain extremely useful for illustration of specific
phenomena. In Fig. 3.30, we see a DSMC calculation for a spherical, uniformly
emitting, nucleus of 2 km in radius. Water is the sole species and the production rate
is 2 kg/s. Profiles of the number density (top right), gas temperature (bottom left) and
velocity (bottom right) are presented out to 10 km from the centre of the sphere. At
the top left of Fig. 3.30, is a 2D slice through the centre of the emitting sphere and
shows the log of the number density colour-coded. Notice that at the surface, the
temperature is marginally over 160 K and a factor of about 0.82 below the temperature of the subliming reservoir (cf Table 3.7). The temperature decrease is rapid,
reaching 70 K within five nucleus radii. At the same time, there is a rapid acceleration (see bottom right) taking the bulk velocity to over 600 m/s very quickly. The
radial velocity approaches the value for the bulk flow measured by Lammerzahl et al.
(1987) between 1000 and 4000 km from the nucleus of 1P/Halley of 800 (Æ50) m
s
À1 . The final speed is not a strong function of production rate in this spherically
symmetric case. This can be seen in Fig. 3.31 which shows the gas speed for total
water production rates covering two orders of magnitude. The speed at five nucleus
radii changes by <20% over this range of Q g .
Another feature of Fig. 3.31 is that gas speeds are approaching their asymptotic
values fairly close to the nucleus. The change in velocity between 8 and 9 km from
the centre of the sphere (3–3.5 radii from the surface) is already <5% km
À1 .
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3 Gas Emissions Near the Nucleus
the total flux is around 61% (as seen in the centre of the jet). In the kinetic case, the
outflow flux ratio is controlled by the square-root of the molecular mass and should
nominally show a similar ratio at source but the water molecules can expand more
quickly through the more diffuse CO 2 resulting in a lower mixing ratio at source.
However, what is more important is that, in the wings of the jets (and particularly
close to the surface in the fluid case), the water mixing ratio is appreciably higher. In
other words, the gas is fractionating. This implies that for jet-like outgassing from a
mixed source, the mixing ratios of gas species measured at one point in the
innermost coma may be substantially different from the mixing ratios of the subliming sources.
It should also be pointed out (although it should be apparent from the previous
discussion) that in low production rate cases, inhomogeneous composition can lead
to differing outflow velocities between species and therefore local densities may not
reflect the actual surface composition but be biased towards heavier, slower moving,
molecules.
3.4.5 Examples of Near-Nucleus Gas Flow
3.4.5.1 Cases with Spherical Sources
The observations of cometary nuclei show them to be highly irregular but calculations with spherical symmetry remain extremely useful for illustration of specific
phenomena. In Fig. 3.30, we see a DSMC calculation for a spherical, uniformly
emitting, nucleus of 2 km in radius. Water is the sole species and the production rate
is 2 kg/s. Profiles of the number density (top right), gas temperature (bottom left) and
velocity (bottom right) are presented out to 10 km from the centre of the sphere. At
the top left of Fig. 3.30, is a 2D slice through the centre of the emitting sphere and
shows the log of the number density colour-coded. Notice that at the surface, the
temperature is marginally over 160 K and a factor of about 0.82 below the temperature of the subliming reservoir (cf Table 3.7). The temperature decrease is rapid,
reaching 70 K within five nucleus radii. At the same time, there is a rapid acceleration (see bottom right) taking the bulk velocity to over 600 m/s very quickly. The
radial velocity approaches the value for the bulk flow measured by Lammerzahl et al.
(1987) between 1000 and 4000 km from the nucleus of 1P/Halley of 800 (Æ50) m
s
À1 . The final speed is not a strong function of production rate in this spherically
symmetric case. This can be seen in Fig. 3.31 which shows the gas speed for total
water production rates covering two orders of magnitude. The speed at five nucleus
radii changes by <20% over this range of Q g .
Another feature of Fig. 3.31 is that gas speeds are approaching their asymptotic
values fairly close to the nucleus. The change in velocity between 8 and 9 km from
the centre of the sphere (3–3.5 radii from the surface) is already <5% km
À1 .
234
3 Gas Emissions Near the Nucleus