SELF-CONVERGENCE OF RADIATIVELY COOLING CLUMPS IN THE INTERSTELLAR MEDIUM

Isolated regions of higher density populate the interstellar medium (ISM) on all scales-from molecular clouds, to the star-forming regions known as cores, to heterogeneous ejecta found near planetary nebulae and supernova remnants. These clumps interact with winds and shocks from nearby energetic sources. Understanding the interactions of shocked clumps is vital to our understanding of the composition, morphology, and evolution of the ISM. The evolution of shocked clumps is well understood in the limiting adiabatic case where physical processes such as self-gravity, heat conduction, radiative cooling, and magnetic fields are ignored. In this paper, we address the issue of evolution and convergence when one of these processes-radiative cooling-is included. Numeric convergence studies demonstrate that the evolution of an adiabatic clump is well captured by roughly 100 cells per clump radius. The presence of radiative cooling, however, imposes limits on the problem due to the removal of thermal energy. Numerical studies which include radiative cooling typically adopt the 100-200 cells per clump radius resolution. In this paper, we present the results of a convergence study for radiatively cooling clumps undertaken over a broad range of resolutions, from 12 to 1536 cells per clump radius, employing adaptive mesh refinement (AMR) in a two-dimensional axisymmetric geometry (2.5 dimensions). We also provide a fully three-dimensional simulation, at 192 cells per clump radius, which supports our 2.5 dimensional results. We find no appreciable self-convergence at similar to 100 cells per clump radius as small-scale differences owing to increasingly resolving the cooling length have global effects. We therefore conclude that self-convergence is an insufficient criterion to apply on its own when addressing the question of sufficient resolution for radiatively cooled shocked clump simulations. We suggest the adoption of alternate criteria to support a statement of sufficient resolution, such as the demonstration of adequate resolution of the cooling layers behind shocks. We discuss associated refinement criteria for AMR codes.