Flux-Limited Diffusion Approximation Models of Giant Planet Formation by Disk Instability. II. Quadrupled Spatial Resolution

While collisional accumulation is nearly universally accepted as the formation mechanism of rock and ice worlds, the situation regarding gas giant planet formation is more nuanced. Gas accretion by solid cores formed by collisional accumulation is the generally favored mechanism, but observations increasingly suggest that gas disk gravitational instability might explain the formation of at least the massive or wide-orbit gas giant exoplanets. This paper continues a series aimed at refining three-dimensional (3D) hydrodynamical models of disk instabilities, where the handling of the gas thermodynamics is a crucial factor. Boss (2017, 2019, 2021) used the $\beta$ cooling approximation (Gammie 2001) to calculate 3D models of disks with initial masses of 0.091 $M_\odot$ extending from 4 to 20 au around 1 $M_\odot$ protostars. Here we employ 3D flux-limited diffusion (FLD) approximation models of the same disks, in order to provide a superior treatment of disk gas thermodynamics. The new models have quadrupled spatial resolution compared to previous 3D FLD models (Boss 2008, 2012), in both the radial and azimuthal spherical coordinates, resulting in the highest spatial resolution 3D FLD models to date. The new models continue to support the hypothesis that such disks can form self-gravitating, dense clumps capable of contracting to form gas giant protoplanets, and suggest that the FLD models yield similar numbers of clumps as $\beta$ cooling models with $\beta \sim$ 1 to $\sim$ 10, including the critical value of $\beta$ = 3 for fragmentation proposed by Gammie (2001).