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

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.