Ku

i

Heliocentric distance (AU)

Heliocentric distance (AU)

Fig. 20. Rotational temperature over heliocentric distance determined from measurements at radio wavelengths of comet Hale-Bopp [25]

leads to variations of the solar flux incident angle over the surface, resulting in differences of the energy available for sublimation.

To study the formation of jets in the inner coma, it is instructive to recall the expansion of a free jet from a nozzle into vacuum (Fig. 21). When gas leaves the nozzle, it expands laterally over a very short distance. Then, it moves along straight streamlines within the isentropic region. The maximum opening angle of the lateral expansion depends on the size of the aperture of the nozzle, the Mach number (gas velocity/sound velocity) and the adiabatic coefficient of the gas. For H2O gas the maximum opening angle is «150°. Figure 22 shows the modeled gas flow field and density above an active region on a spherical nucleus [132]. The wide lateral expansion of the gas jet around the nucleus can be seen. The gas density is also shown on a somewhat larger scale in Fig. 23.

Dust particles in the gas flow decouple from the streaming gas when the density decreases, as explained above. Therefore, the lateral expansion of the dust flow is less than for the gas. The decoupling of the dust depends on the particle size and density. Small grains show wider lateral expansion than large grains. Figure 23 shows the gas and dust density distribution above an active surface region for comparison. The difference is obvious, the lateral expansion of larger (10 |m radius) dust particles is much smaller than for the gas. Nevertheless, the dust jet above an active region is still a relatively wide feature.

Filaments

In situ images of comet Halley show very narrow structures, called filaments (Fig. 30), which become clearly visible after some contrast enhancing image processing. They have narrow opening angles <10° and column density enhancements above the coma background of only a factor of two [203]. As normal gas and dust jets are expected to show much wider opening angles (see above), this observation stimulated research to reproduce narrow straight flow structures.

Fig. 21. Schematic view of the expansion of a free jet into vacuum [132]

Fig. 22. Gas flow field and density distribution [132] for an active area with constant production rate on a spherical nucleus. Note the wide lateral expansion of the gas jet around the nucleus

Fig. 22. Gas flow field and density distribution [132] for an active area with constant production rate on a spherical nucleus. Note the wide lateral expansion of the gas jet around the nucleus

Fig. 23. Gas density distribution (top) and distribution for 10 |J,m dust particles (bottom) [132] in the inner coma above an active area on a spherical nucleus. Note the wide lateral expansion of the gas and the more confined distribution of the larger dust particles
Fig. 24. Gas and dust density distribution for a jet expanding into a background gas [132]. Upper left: gas density; Upper right: dust particles with 1000 |J,m radius; Lower left: 30 |J,m radius; Lower right: 1 |J,m radius

To address the formation of narrow, straight filaments in the inner coma, we look at the expansion of gas into a background gas. In such a case, the gas flow is confined by the gas background, inhibiting the lateral expansion of the flow. Close to the boundaries, between outstreaming and background gas, shock systems form. Figure 24 shows the effect of the lateral expansion into a background for gas and dust particles of three sizes. At the jet boundaries, gas density enhancements form in the shock system. These enhancements would give the appearance of filaments or very confined jets in images of the near-nucleus region. The formation of narrow structures is even more pronounced for the dust. However, for comparison with observations, the integrated intensity along the line-of-sight must be computed. Looking at the coma from different aspect angles, the appearance of the interaction regions can be very different, and sometimes the narrow filament-like features produced in the interaction region are not visible (Fig. 25). Therefore, filaments formed by the interaction of gas flows may disappear as the viewing geometry changes, for example from an orbiting spacecraft or by the rotation of a nucleus as seen from Earth.

To summarize we note that

• The interaction of an outstreaming gas with a gas background produces density enhancements at the interaction region giving the appearance of filaments.

• These filaments are not located directly above an active region on the surface, but at the jet/background boundary.

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