Formation of Giant Planets by Gas Disk Gravitational Instability on Wide Orbits around Protostars with Varied Masses. II. Quadrupled Spatial Resolution and Beta Cooling

Abstract

Exoplanet demographics are sufficiently advanced to provide important constraints on theories of planet formation. While core and pebble accretion are preferred for rocky and icy planets, there appears to be a need for gas disk gravitational instability (GDGI) to play a role in the formation of M-dwarf gas giants and those orbiting at large distances. Here we present GDGI models that go beyond those presented by Boss (2011) dealing with the formation of wide-orbit gas giants. The new models use quadrupled spatial resolution, in both the radial and azimuthal directions, to reduce the effects of finite spatial resolution. The new models also employ the β cooling approximation, instead of the diffusion approximation used by Boss (2011), in order to push the models further in time. As in Boss (2011), the central protostars have masses of 0.1, 0.5, 1.0, 1.5, or 2.0 M ⊙, surrounded by disks with masses ranging from 0.019 M ⊙ to 0.21 M ⊙. For each case, two models are computed, one with an initial minimum Toomre Q stability value ranging from 1.1 to 1.7, and one with a higher initial disk temperature, resulting in the initial minimum Q ranging from 2.2 to 3.4. These new models continue to show that GDGI can explain the formation of gas giants at distances of ∼30 to ∼50 au on eccentric orbits (e less than ∼0.2), though the number formed drops to 0 as the protostar mass decreases to 0.1 M ⊙.