3D hydrodynamics simulations of core convection in supermassive main-sequence stars

Supermassive stars are Population III stars with masses exceeding $10^4\, {\rm M}_{\odot }$ that could be the progenitors of the first supermassive black holes. Their interiors are in a regime where radiation pressure dominates the equation of state. In this work, we use the explicit gas dynamics code PPMSTAR to simulate the hydrogen-burning core of a $10^4\, {\rm M}_{\odot }$ supermassive main-sequence star. These are the first three-dimensional hydrodynamics simulations of core convection in supermassive stars. We perform a series of 10 simulations at different heating rates and on Cartesian grids with resolutions of 768³, 1152³, and 1728³. We examine different properties of the convective flow, including its large-scale morphology, its velocity spectrum, and its mixing properties. We conclude that the radiation pressure-dominated nature of the interior does not noticeably affect the behaviour of convection compared to the case of core convection in a massive main-sequence star where gas pressure dominates. Our simulations also offer support for the use of mixing-length theory in one-dimensional models of supermassive stars.