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

In this and two subsequent papers we develop analytic solutions for the rate of evaporative mass loss from an isolated spherical cloud embedded in a hot tenuous gas. In the present paper we consider systems in which the effects of radiation and magnetic fields may be neglected; these effects will be considered in the two subsequent papers. It is pointed out that in many cases of interest the classical form of the thermal conduction is inapplicable and an upper bound to the heat flux which may be carried by the electrons is derived which is substantially lower than most previous estimates. Eigenvalues of the time-independent energy conservation equations are found both in the case where the classical conduction is applicable throughout the interface and in the case where the heat flux reaches its limiting value. (We refer to this as saturation.) The dynamics of the flow from the cloud is analyzed in both cases, and the use of the time-independent equations is justified. The theory is compared with the theory of thermal conduction fronts described by McKee and Cowie. Finally we consider the application of the theory to clouds within supernova remnants where anisotropy and dynamical effects are important. Discussion of the applications of these results is deferred to Paper II, where the effects of radiation are considered