### The evolution of the mass ratio of accreting binaries: the role of gas temperature

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We explore an unresolved controversy in the literature about the accuracy of Smoothed Particle Hydrodynamics (SPH) in modeling the accretion of gas onto a binary system, a problem with important applications to the evolution of proto-binaries as well as accreting binary super massive black holes. It has previously been suggested that SPH fails to model the flow of loosely bound material from the secondary to primary Roche lobe and that its general prediction that accretion drives mass ratios upwards is numerically flawed. Here we show with 2D SPH that this flow from secondary to primary Roche lobe is a sensitive function of gas temperature and that this largely explains the conflicting claims in the literature which have hitherto been based on either ‘cold’ SPH simulations or ‘hot’ grid based calculations. We present simulations of a specimen ‘cold’ and ‘hot’ accretion scenario which are numerically converged and evolved into a steady state. Our analysis of the conservation of the Jacobi integral of accreting particles indicates that our results are not strongly compromised by numerical dissipation. We also explore the low resolution limit and find that simulations where the ratio of SPH smoothing length to disc scale height at the edge of the circumsecondary is less than 1 accurately capture binary accretion rates.