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An Efficient Radiative Cooling Approximation for Use in Hydrodynamic Simulations

To make relevant predictions about observable emission, hydrodynamical simulation codes must employ schemes that account for radiative losses, but the large dimensionality of accurate radiative transfer schemes is often prohibitive. Stamatellos and collaborators introduced a scheme for smoothed particle hydrodynamics (SPH) simulations based on the notion of polytropic pseudo-clouds that uses only local quantities to estimate cooling rates. The computational approach is extremely efficient and works well in cases close to spherical symmetry, such as in star formation problems. Unfortunately, the method, which takes the local gravitational potential as an input, can be inaccurate when applied to non-spherical configurations, limiting its usefulness when studying disks or stellar collisions, among other situations of interest. Here, we introduce the "pressure scale height method," which incorporates the fluid pressure scale height into the determination of column densities and cooling rates, and show that it produces more accurate results across a wide range of physical scenarios while retaining the computational efficiency of the original method. The tested models include spherical polytropes as well as disks with specified density and temperature profiles. We focus on applying our techniques within an SPH code, although our method can be implemented within any particle-based Lagrangian or grid-based Eulerian hydrodynamic scheme. Our new method may be applied in a broad range of situations, including within the realm of stellar interactions, collisions, and mergers.