Monte Carlo particle-trajectory models for neutral cometary gases. I - Models and equations. II - The spatial morphology of the Lyman-alpha coma

The Monte Carlo particle-trajectory models for the distributions of neutral gases in cometary atmospheres, developed in original form several years ago, have been greatly extended and generalized. In a Monte Carlo particle-trajectory model (MCPTM) the spatial distribution of a neutral cometary species is determined by calculating the explicit trajectories of many individual particles following the chain of parent vaporization, coma outflow, photodissociations, collisions, and decay through the appropriate number of generations. In this paper the mathematical derivations of the various methods employed in the MCPTM are presented in detail, and the application of the MCPTM to the calculation of the photochemical heating of the inner coma through the partial thermalization of cometary hydrogen atoms produced by the photodissociation of water is discussed.