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In the core accretion hypothesis, giant planets form by gas accretion ontosolid protoplanetary cores. The minimum (or critical) core mass to form a gasgiant is typically quoted as 10 Earth masses. The actual value depends onseveral factors: the location in the protoplanetary disk, atmospheric opacity,and the accretion rate of solids. Motivated by ongoing direct imaging searchesfor giant planets, this study investigates core mass requirements in the outerdisk. To determine the fastest allowed rates of gas accretion, we considersolid cores that no longer accrete planetesimals, as this would heat thegaseous envelope. Our spherical, two-layer atmospheric cooling model includesan inner convective region and an outer radiative zone that matches onto thedisk. We determine the minimum core mass for a giant planet to form within atypical disk lifetime of 3 Myr. The minimum core mass declines with diskradius, from ~8.5 Earth masses at 5 AU to ~3.5 Earth masses at 100 AU, withstandard interstellar grain opacities. Lower temperatures in the outer diskexplain this trend, while variations in disk density are less influential. Atall distances, a lower dust opacity or higher mean molecular weight reduces thecritical core mass. Our non-self-gravitating, analytic cooling model revealsthat self-gravity significantly affects early atmospheric evolution, startingwhen the atmosphere is only ~10% as massive as the core.

On the Minimum Core Mass for Giant Planet Formation at Wide Separations