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Hot phase generation by supernovae: resolution, chemistry and thermal conduction

Supernovae (SN) generate hot gas in the interstellar medium (ISM), help setting the ISM structure and support the driving of outflows. It is important to resolve the hot gas generation for galaxy formation simulations at solar mass and sub-parsec resolution which realise individual supernova (SN) explosions with ambient densities varying by several orders of magnitude in a realistic multi-phase ISM. We test resolution requirements by simulating SN blast waves at three metallicities ($Z = 0.01, 0.1$ and $1 Z_{\odot}$), six densities and their respective equilibrium chemical compositions ($n=0.001$ cm$^{-3}$ - $100$ cm$^{-3}$), and four mass resolutions ($0.1$ - $100$ M$_{\odot}$), in three dimensions. We include non-equilibrium cooling and chemistry, a homogenous interstellar radiation field, and shielding with a modern pressure-energy smoothed particle hydrodynamics (SPH) method including isotropic thermal conduction and a meshless-finite-mass (MFM) solver. We find stronger resolution requirements for chemistry and hot phase generation than for momentum generation. While at $10$ M$_{\odot}$ the radial momenta at the end of the Sedov phase start converging, the hot phase generation and chemistry require higher resolutions to represent the neutral to ionised hydrogen fraction at the end of the Sedov phase correctly. Thermal conduction typically reduces the hot phase by $0.2$ dex and has little impact on the chemical composition. In general, our $1$, and $0.1$ M$_{\odot}$ results agree well with previous numerical and analytic estimates. We conclude that for the thermal energy injection SN model presented here resolutions higher than $10$ M$_{\odot}$ are required to model the chemistry, momentum and hot phase generation in a multi-phase ISM.