Numerical simulations of the random angular momentum in convection: Implications for supergiant collapse to form black holes

During the core collapse of massive stars that do not undergo a canonical energetic explosion, some of the hydrogen envelope of a red supergiant (RSG) progenitor may infall on to the newborn black hole (BH). Within the ATHENA++ framework, we perform 3D, hydrodynamical simulations of idealized models of supergiant convection and collapse in order to assess whether the infall of the convective envelope can give rise to rotationally supported material, even if the star has zero angular momentum overall. Our dimension-less, polytropic models are applicable to the optically thick hydrogen envelope of non-rotating RSGs and cover a factor of 20 in stellar radius. At all radii, the specific angular momentum due to random convective flows implies associated circularization radii of 10-1500 times the innermost stable circular orbit of the BH. During collapse, the angular momentum vector of the convective flows is approximately conserved and is slowly varying on the time-scale relevant to forming discs at small radii. Our results indicate that otherwise failed explosions of RSGs lead to the formation of rotationally supported flows that are capable of driving outflows to large radii and powering observable transients. When the BH is able to accrete most of the hydrogen envelope, the final BH spin parameter is ~ 0.5, even though the star is non-rotating. For fractional accretion of the envelope, the spin parameter is generally lower and never exceeds 0.8. We discuss the implications of our results for transients produced by RSG collapse to a black hole.