The photochemistry and dynamics of a dusty cometary atmosphere

A self-consistent solution of the dynamical and thermal structure of an H₂O-dominated, two-phase, dusty-gas cometary atmosphere has been obtained by solving the simultaneous set of differential equations representing conservation of number density, momentum and energy together with the transfer of solar radiation in the streams responsible for the major photolytic processes and the heating of the nucleus. The validity of the model is restricted to the collision-dominated region where all the gas species are assumed to attain a common velocity and common temperature. Two models are considered for the transfer of solar radiation through the circum-nuclear dust halo. In the first only the direct extinction by the dust is considered. In the second, the finding of some recent models, that the diffuse radiation field due to multiple scattering by the dust halo more or less compensates for radiation removed by direct absorption when the optical depth is near unity, is approximated by neglecting the attenuation of the radiation by the dust altogether.As has been shown earlier, the presence of dust results in a transonic solution, and it is obtained by a two-step iterative procedure which makes use of the asymptotic behaviour of the radiation fields sufficiently far from the nucleus and a regularity condition at the sonic point.The calculations were performed for a medium sized comet (R _n =2.5 km) having a dust to gas production rate ratio of unity, at a heliocentric distance of 1 AU. The dust grains were assumed to be of the same radius (1), of low density (1g cm^–3) and be strongly absorbing (having the optical properties of magnetite).The main effect of the dust on the cometary atmosphere is dynamic. While the dust-gas coupling persists to about 20R _n , the strong throat effect of the dust friction on the gas causes the latter to go supersonic quite rapidly. Consequently the sub-sonic region around the nucleus is very thin, varying between 45 and 85m in the two models considered. On the other hand, while this highly absorbing dust has a temperature substantially above that of the gas in the inner coma, heat exchange between them does not significantly change the temperature profile of the gas. This is because of the predominance of the expansion cooling, and even more importantly, the IR-cooling by H₂O, in the inner coma. Consequently, the gas temperature goes through a strong inversion, as in the dust-free case, achieving a temperature as low as about 6K within about 50km of the nucleus, before increasing to about 700K atr=10⁴km, due to the high efficiency of photolytic heating over the cooling process in the outer coma. The Mach number achieves a maximum value of about 10 at the distance of the temperature minimum, thereafter steadily decreasing to a value of about 2.5 atr10⁴km.It is shown that while the dust attenuation has a strong effect on the production rate of H₂O, it also has an interesting effect on the electron density profile. It increases the electron density in the inner coma over the unattenuated case, while at the same time, decreasing it in the outer coma. In conclusion, the limitations of the present model and the necessity to extend it using a multi-fluid approach are discussed.