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collisional dominated

Fig. 12. Illustration of the principle processes in a cometary coma for a Halley-type comet near rh = 1 AU

expected to drop even lower, down to about 20 K. Heating mechanisms such as gas-dust interaction or recondensation are discussed to explain the somewhat higher observed gas coma temperatures at these distances [52].

• At larger nucleocentric distances (103-104 km), heating of the gas by pho-tolytic processes is important resulting in an increasing gas temperature in the intermediate coma. The main heating process is photo-dissociation of water molecules into OH and H. The dissociation provides an excess energy to the daughter products, which results in molecule excess velocities in the order of 18kms_1 for H and about 1.09kms-1 for OH molecules (see [47] for details on excess velocities and branching ratios of H2O photodissociation).

• At large nucleocentric distances, radiative cooling of the coma molecules decreases the temperature again.

The Choice of Mathematical Description

Above the surface, a Maxwellian velocity distribution is established in the sublimated gas after a few collisions. For a comet like Halley, the flow is dominated by collisions for the first kilometers in the coma and can be described by hydrodynamic equations. At distances beyond several 104 km, however, collisions are rare due to the low gas densities, and the coma can be described as a free molecular flow. At such large distances, the influence of solar gravitation and radiation pressure is important. Solar radiation pressure accelerates the gas into the anti-solar direction and leads to a deviation of the coma from spherical shape on a large scale (Fig. 13).

Transition region,

Transition region,

Fig. 13. Illustration of the principle flow regimes in a cometary coma for a Halley-type comet near rh = 1 AU

Fig. 13. Illustration of the principle flow regimes in a cometary coma for a Halley-type comet near rh = 1 AU

In general, a hydrodynamic description of the flow can be applied if the mean free path between collisions of two gas molecules, A, is small against a characteristic length of the system, L, i.e. A < L, with

V 2an

On the surface we can write:

Here, a is the collisional cross-section of the gas molecules, n the gas number density, u the gas velocity at the surface, and Z the surface sublimation rate (molecules s-1 cm-2).

Often the Knudsen number I\ = is used to characterize the flow regime (Fig. 13 and 14). Inviscid hydrodynamics can be used for K < 0.1. For K > 0.1 the flow becomes viscous but is still hydrodynamic (described by the Navier-Stokes equations), and for K > 10 we have to treat the flow as free molecular outflow.

Assuming L to be equivalent to the nucleus radius, rnucieus, the size of the collisionally dominated coma is about 103-104 km. The choice of rnucleus as a characteristic length L is somewhat artificial. Alternatively, the radial distance to the nucleus, r, is sometimes used.

Whenever a description by hydrodynamics is not applicable, Monte-Carlo models provide an alternative approach, although they are computationally time intensive. In a Monte-Carlo approach, the real gas is approximated by a large number of simulated molecules moving in a grid space and with time. Position, velocity, and energy exchange by collisions between particles are computed and monitored. Monte-Carlo approaches are, for example, mandatory for modeling the huge hydrogen coma of comets (e.g., [47]). They are also needed when modeling the outer regions of a coma or weakly active comets with low gas densities that never form a collisionally dominated coma region. If hydrodynamics can be applied, it is more efficient, but Monte-Carlo ioL ,io= ,io! , ioJ I ig5 io6

distance [km]

distance [km]

K<ai

0.1 < K < 10 K> 10

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