Circumplanetary Disk Dynamics in the Isothermal and Adiabatic Limits

Circumplanetary disks (CPDs) may be essential to the formation of planets, regulating their spin and accretion evolution. We perform a series of 3D hydrodynamics simulations in both the isothermal and adiabatic limits to systematically measure the rotation rates, sizes, and masses of CPDs as functions of $q_{\rm thermal}$, the ratio of the planet mass to the disk thermal mass. Our $q_{\rm thermal}$ ranges from 0.1 to 4; for our various disk temperatures, this corresponds to planet masses between 1 Earth mass and 4 Jupiter masses. Within this parameter space, we find that isothermal CPDs are disky and bound within $\sim$10\% of the planet's Bondi radius $r_{\rm B}$, with the innermost $\sim0.05\,r_{\rm B}$ in full rotational support. Adiabatic CPDs are spherical (therefore not actually "disks"), bound within $\sim0.2\,r_{\rm B}$, and mainly pressure-supported with rotation rates scaling linearly with $q_{\rm thermal}$; extrapolation suggests full rotational support of adiabatic envelopes at $\sim10\,q_{\rm thermal}$. Fast rotation and 3D supersonic flow render isothermal CPDs significantly different in structure from --- and orders of magnitude less massive than --- their 1D isothermal hydrostatic counterparts. Inside a minimum-mass solar nebula, even a maximally cooled, isothermal CPD around a 10 Earth-mass core may have less than 1 Earth mass, suggesting that gas giant formation may hinge on angular momentum transport processes in CPDs. Our CPD sizes and masses appear consistent with the regular satellites orbiting solar system giants.