The Endgame of Gas Giant Formation: Accretion Luminosity and Contraction Post-Runaway

Abstract

Giant planets are thought to form by runaway gas accretion onto solid cores. Growth must eventually stop running away, ostensibly because planets open gaps (annular cavities) in their surrounding discs. Typical models stop runaway by artificially capping the accretion rate and lowering it to zero over an arbitrarily short time-scale. In reality, post-runaway accretion persists as long as the disc remains. During this final and possibly longest phase of formation, when the planet is still emerging from the disc, its mass can more than double, and its radius contracts by orders of magnitude. By drawing from the theory of how gaps clear, we find that post-runaway accretion luminosities diverge depending on disc viscosity: luminosities fall in low-viscosity discs but continue to rise past runaway in high-viscosity discs. This divergence amounts to a factor of $10^2$ by the time the disc disperses. Irrespective of the specifics of how planets interact with discs, the observed luminosity and age of an accreting planet can be used to calculate its instantaneous mass, radius, and accretion rate. We perform this exercise for the planet candidates embedded within the discs orbiting PDS 70, HD 163296, and MWC 758, inferring masses of $1-10\, M_{\rm J}$, accretion rates of $0.1-10\, M_{\rm J}$/Myr, and radii of $1-10\, R_{\rm J}$. Our radii are computed self-consistently from the planet's concurrent contraction and accretion and do not necessarily equal the value of $2R_{\rm J}$ commonly assumed; in particular, the radius depends on the envelope opacity as $R \propto \kappa^{0.5}$.