The evaporation of spherical clouds in a hot gas. I - Classical and saturated mass loss rates

Analytic solutions are obtained for the rate of evaporative mass loss from an isolated spherical cloud embedded in a hot tenuous gas, neglecting effects of radiation and magnetic fields. Consideration is given only to the case of spherical clouds, where the evaporative mass-loss rate is an eigenvalue of the time-independent energy-conservation equation. The upper bound on the heat flux which may be carried by electrons is found to be smaller than previously expected, it is assumed that the exact heat flux should closely approximate this maximum value in collisionless gases, and such a theory is shown to give good numerical agreement with solar-wind observations. A straightforward solution is obtained for those cases where the classical thermal-conduction formula is applicable throughout the interface, and limitations are given under which analytic solutions can be found when the classical formula does not apply throughout the interface. The results of the present theory are compared with those of a previous and less accurate analysis which considered conducting fronts analogous to ionization fronts. Cloud evaporation within supernova remnants is discussed, and it is concluded that the present results should provide a reasonable approximation even in such an extreme case.