Evaporation and condensation of spherical interstellar clouds. Self-consistent models with saturated heat conduction and cooling

Aims. The fate of interstellar clouds embedded in a hot tenuous medium depends on whether the clouds suffer from evaporation or whether material condensates onto the clouds. The knowledge of the evaporation or condensation rates of interstellar clouds at rest is therefore of prime importance for their further evolution. Analytic solutions for the rate of evaporative mass loss from an isolated spherical cloud embedded in a hot tenuous gas are deduced by Cowie & McKee (1977, ApJ, 211, 135). Their approach is limited to the integration of the time-independent energy conservation equation for the heat-conductive interface. Therefore it is crucial to test the validity of the analytical results for more realistic interstellar conditions. This requires that the full hydrodynamical equations must be treated taking the whole cloud into account with a sufficiently large hot-gas reservoir. Methods. By two-dimensional numerical simulations in an Eulerian, explicit hydrodynamical grid the evolution of interstellar clouds with different internal density structures and surrounded by a hot plasma is simulated. Self-gravity, interstellar heating and cooling effects and heat conduction by electrons are added. We use the classical thermal conductivity of a fully ionized hydrogen plasma proposed by Spitzer and a saturated heat flux according to Cowie and McKee in regions where the mean free path of the electrons is large compared to the temperature scaleheight. Results. Using pure hydrodynamics and taking only the classical heat flux into account, we can reproduce the Cowie and McKee analytical results. If we allow for heat flux saturation the evaporation rate is reduced, but in the simulations even to about one order of magnitude below the predicted saturated one. This happens because the saturated heat flux is density dependent and due to the mixing of the two phases, the warm cloud material on one side and the hot intercloud medium, also the density distribution changes drastically there during the simulation. And this cannot be considered in the analytical study. This main result still holds if we add self gravity or choose another cloud density structure while keeping the cloud radius and temperature of the cloud edge constant. As a further issue the evolution changes, however, totally for more realistic conditions when interstellar heating and cooling effects stabilize the self-gravity. The clouds' evaporation then turns into condensation, because the additional energy input due to heat conduction can be transported away from the interface and radiated off very efficiently from the cloud's inner parts. Conclusions. The assumption of pure classical heat conduction is invalid for the description of the evolution of interstellar clouds in a hot tenuous gas. The consideration of a limited saturated heat flux is inevitable for this kind of simulations and leads to a dramatic decrease of the evaporation rate. And even more realisticly with radiative cooling heat conduction leads to condensation in contradiction to analytical predictions which require evaporation. This has two consequences: Interstellar clouds are stabilized against evaporation. On the other hand this provides an efficient way to accrete and mix intercloud material into clouds.