2021ApJ...911..146B

Observations support the hypothesis that gas disk gravitational instability might explain the formation of massive or wide-orbit gas giant exoplanets. The situation with regard to Jupiter-mass exoplanets orbiting within ∼20 au is more uncertain. Theoretical models yield divergent assessments often attributed to the numerical handling of the gas thermodynamics. Boss used the β cooling approximation to calculate three-dimensional hydrodynamical models of the evolution of disks with initial masses of 0.091 M_☉ extending from 4 to 20 au around 1 M_☉ protostars. The models considered a wide range (1-100) of β cooling parameters and started from an initial minimum Toomre stability parameter of Q_i = 2.7 (gravitationally stable). The disks cooled down from initial outer disk temperatures of 180 K to as low as 40 K as a result of the β cooling, leading to fragmentation into dense clumps, which were then replaced by virtual protoplanets (VPs) and evolved for up to ∼500 yr. The present models test the viability of replacing dense clumps with VPs by quadrupling the spatial resolution of the grid once dense clumps form, sidestepping in most cases VP insertion. After at least ∼200 yr of evolution, the new results compare favorably with those of Boss: similar numbers of VPs and dense clumps form by the same time for the two approaches. The results imply that VP insertion can greatly speed disk instability calculations without sacrificing accuracy.