Self-Convergence of Radiatively Cooling Clumps in the Interstellar Medium

Abstract

Isolated regions of higher density populate the 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 are wellunderstood 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 wellcaptured 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 1,536 cells per clump radius, employing adaptive mesh refinement (AMR) in a 2D axisymmetric geometry (2.5D). We also provide a fully 3D simulation, at 192 cells per clump radius, which supports our 2.5D results. We find no appreciable self-convergence at ∼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 an associated refinement criteria for AMR codes.

Radiative Interaction of Shocks With Small Interstellar Clouds as a Pre-Stage to Star Formation

“…Yirak et al (2010), however, pointed out the need to resolve the cooling length l cool in radiative shock-cloud interactions and criticized some earlier studies (Mellema et al 2002;Fragile et al 2004) with strong cooling for being highly underresolved in this regard, leading to reduced cooling and dampened RT and KH instabilities as a consequence thereof. Although this problem is mitigated by our different set of parameter values (e.g., much smaller cloud), due to computational constraints, we are still forced to tolerate a somewhat underresolved cooling length of 0.64 cell widths.…”

“…Radiative cooling has only been incorporated more recently 2 (e.g., Mellema et al 2002;Fragile et al 2004;Orlando et al 2005Orlando et al , 2008Yirak et al 2010;van Loo et al 2007van Loo et al , 2010. Radiative cooling can change the interaction drastically by removing thermal energy and pressure from the shocked cloud material.…”

The interaction of a magnetohydrodynamical shock with a filament

“…Klein et al 1994;Nakamura et al 2006), with more complex cases requiring even higher resolutions (e.g. Yirak et al 2010). However, it is very computationally expensive to run 3D simulations to such high resolutions.…”

“…Mac Low et al 1994;Shin-S., Stone & Snyder 2008), radiative cooling (e.g. Mellema, Kurk & Röttgering 2002;Fragile et al 2004;Yirak, Frank & Cunningham 2010) and thermal conduction (e.g. Orlando et al 2005Orlando et al , 2008.…”

The impact of recent advances in laboratory astrophysics on our understanding of the cosmos

“…Only a handful of multiple clump studies have been published (Fragile et al 2004;Yirak et al 2008). Because 3-D simulation studies are often resolution limited (Yirak et al 2011) laboratory studies can offer relatively clean platforms for deeper exploration of shock-clump interactions. A robust literature reporting a host of shock-clump high energy density laboratory astrophysics (HEDLA) studies has emerged over the last decade.…”