Minimum core masses for giant planet formation with realistic equations of state and opacities

Abstract

Giant planet formation by core accretion requires a core that is sufficiently massive to trigger runaway gas accretion in less than the typical lifetime of protoplanetary disks. We explore how the minimum required core mass, M crit, depends on a non-ideal equation of state (EOS) and on opacity changes due to grain growth across a range of stellocentric distances from 5-100 AU. This minimum M crit applies when planetesimal accretion does not substantially heat the atmosphere. Compared to an ideal gas polytrope, the inclusion of molecular hydrogen (H2) dissociation and variable occupation of H2 rotational states increases M crit. Specifically, M crit increases by a factor of ∼2 if the H2 spin isomers, ortho- and parahydrogen, are in thermal equilibrium, and by a factor of ∼2-4 if the ortho-to-para ratio is fixed at 3:1. Lower opacities due to grain growth reduce M crit. For a standard disk model around a Solar mass star, we calculate M crit ∼ 8 M ⊕ at 5 AU, decreasing to ∼5 M ⊕ at 100 AU, for a realistic EOS with an equilibrium ortho-to-para ratio and for grain growth to centimeter-sizes. If grain coagulation is taken into account, M crit may further reduce by up to one order of magnitude. These results for the minimum critical core mass are useful for the interpretation of surveys that find exoplanets at a range of orbital distances.