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

TL;DR

This study investigates how realistic equations of state and grain growth affect the minimum core mass needed for giant planet formation via core accretion across 5-100 AU, providing updated thresholds for different conditions.

Contribution

It quantifies the impact of non-ideal gas physics and grain growth on the critical core mass, offering more accurate estimates for planet formation models.

Findings

M_crit increases by a factor of ~2 with equilibrium ortho-para H_2 ratio.

Lower opacities due to grain growth reduce M_crit.

At 5 AU, M_crit is about 8 Earth masses, decreasing to 5 Earth masses at 100 AU.

Abstract

Giant planet formation by core accretion requires a core that is sufficiently massive to trigger runaway gas accretion in less that the typical lifetime of protoplanetary 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 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 (H_2) dissociation and variable occupation of H_2 rotational states increases M_crit. Specifically, M_crit increases by a factor of ~2 if the H_2 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_Earth at 5 AU, decreasing to ~5 M_Earth at 100 AU, for a realistic EOS with an equilibrium ortho-to-para ratio and for grain growth to cm-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.