Supermassive black hole dynamics during galaxy mergers is crucial in determining the rate of black hole mergers and cosmic black hole growth. As simulations achieve higher resolution, it becomes important to assess whether the black hole dynamics is influenced by the treatment of the interstellar medium in different simulation codes. We here compare simulations of black hole growth in galaxy mergers with two codes: the Smoothed Particle Hydrodynamics code Gasoline, and the Adaptive Mesh Refinement code Ramses. We seek to identify predictions of these models that are robust despite differences in hydrodynamic methods and implementations of sub-grid physics. We find that the general behavior is consistent between codes. Black hole accretion is minimal while the galaxies are well-separated (and even as they fly-by within 10 kpc at first pericenter). At late stages, when the galaxies pass within a few kpc, tidal torques drive nuclear gas inflow that triggers bursts of black hole accretion accompanied by star formation. We also note quantitative discrepancies that are model-dependent: our Ramses simulations show less star formation and black hole growth, and a smoother gas distribution with larger clumps and filaments, than our Gasoline simulations. We attribute these differences primarily to the sub-grid models for black hole fueling and feedback and gas thermodynamics. The main conclusion is that differences exist quantitatively between codes, and this should be kept in mind when making comparisons with observations. However, reassuringly, both codes capture the same dynamical behaviors in terms of triggering of black hole accretion, star formation, and black hole dynamics.
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