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 J , accretion rates of 0.1-10 M J /Myr, and radii of 1-10 R J . Our radii are computed self-consistently from the planet's concurrent contraction and accretion and do not necessarily equal the value of 2R J commonly assumed; in particular, the radius depends on the envelope opacity as R ∝ κ 0.5 .

Breaking the centrifugal barrier to giant planet contraction by magnetic disc braking

“…If nothing else, the dipole geometry of the magnetic field, whose energy density dominates at r < R t , should help to enforce a roughly spherical magnetosphere. In Ginzburg & Chiang (2019a) we explained that during post-runaway accretion the planet adjusts its contraction to satisfy t KH = M/ M. This condition was derived neglecting spin angular momentum; however, we will find below that magnetic spin-down is efficient and that contraction can proceed on the KH time-scale, with the planet radiating away the accretion luminosity L = GM M/R. Using this relation, and substituting B from equation (3), we rewrite equation…”

“…1 we plot four example evolutionary tracks for spin and magnetic field. The tracks represent different post-runaway cooling and accretion models, as computed in figs 1-4 of Ginzburg & Chiang (2019a). In that paper, we parametrized the post-runaway accretion rate M with a power law M/ M ∝ M β , and numerically solved the planet's concurrent accretion and contraction history.…”

“…In the β = 15 models, which are inspired by planets opening gaps in practically inviscid discs, gas accretion drops more drastically after the end of runaway growth, producing planets with a final mass slightly less than Jupiter (0.8 M J ). Ginzburg & Chiang (2019a). Time is measured since the end of runaway growth, after which the planet mass doubles on a time-scale that grows with mass as M/ M ∝ M β .…”

“…Both of these effects can put an end to runaway growth (Lin & Papaloizou 1993;Kley 1999;Tanigawa & Ikoma 2007;Lissauer et al 2009;Tanigawa & Tanaka 2016;Ginzburg & Chiang 2019b;Lee 2019). Post-runaway planetary accretion is not zero; it persists up to the eventual dispersal of the disc in a few million years' time (Mamajek 2009;Pfalzner et al 2014), and can be responsible for doubling the planet's mass or more (Mordasini et al 2012;Ginzburg & Chiang 2019a).…”

“…In the post-runaway phase, because of insufficient gas supply, the planet no longer fills the Bondi/Hill radius but detaches from the nebula to contract on the KH timescale (Bodenheimer et al 2000;Mordasini et al 2012Mordasini et al , 2017Ginzburg & Chiang 2019a). Previous one-dimensional models assumed the planet is free to shrink by orders of magnitude until its radius is comparable to that of Jupiter.…”