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Giant planet formation by core accretion requires a core that is sufficientlymassive to trigger runaway gas accretion in less that the typical lifetime ofprotoplanetary disks. We explore how the minimum required core mass, M_crit,depends on a non-ideal equation of state and on opacity changes due to graingrowth, across a range of stellocentric distances from 5-100 AU. This minimumM_crit applies when planetesimal accretion does not substantially heat theatmosphere. Compared to an ideal gas polytrope, the inclusion of molecularhydrogen (H_2) dissociation and variable occupation of H_2 rotational statesincreases M_crit. Specifically, M_crit increases by a factor of ~2 if the H_2spin isomers, ortho- and parahydrogen, are in thermal equilibrium, and by afactor of ~2-4 if the ortho-to-para ratio is fixed at 3:1. Lower opacities dueto grain growth reduce M_crit. For a standard disk model around a Solar massstar, we calculate M_crit ~ 8 M_Earth at 5 AU, decreasing to ~5 M_Earth at 100AU, for a realistic EOS with an equilibrium ortho-to-para ratio and for graingrowth to cm-sizes. If grain coagulation is taken into account, M_crit mayfurther reduce by up to one order of magnitude. These results for the minimumcritical core mass are useful for the interpretation of surveys that findexoplanets at a range of orbital distances.

Minimum Core Masses for Giant Planet Formation With Realistic Equations of State and Opacities