Luminosity of young Jupiters revisited

Massive cores make hot planets

Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
e-mail: mordasini@mpia.de

Received: 1 April 2013
Accepted: 22 June 2013

Abstract

Context. The intrinsic luminosity of young Jupiters is of high interest for planet formation theory. It is an observable quantity that is determined by important physical mechanisms during formation, namely, the structure of the accretion shock and, even more fundamentally, the basic formation mechanism (core accretion or gravitational instability).

Aims. Our aim is to study the impact of the core mass on the post-formation entropy and luminosity of young giant planets forming via core accretion with a supercritical accretion shock that radiates all accretion shock energy (cold accretion).

Methods. For this, we conduct self-consistently coupled formation and evolution calculations of giant planets with masses between 1 and 12 Jovian masses and core masses between 20 and 120 Earth masses in the 1D spherically symmetric approximation.

Results. As the main result, it is found that the post-formation luminosity of massive giant planets is very sensitive to the core mass. An increase in the core mass by a factor 6 results in an increase in the post-formation luminosity of a 10-Jovian mass planet by a factor 120, indicating a dependency as ${\mathit{M}}_{\mathrm{core}}^{\mathrm{2}\mathrm{-}\mathrm{3}}$. Due to this dependency, there is no single well-defined post-formation luminosity for core accretion, but a wide range, even for completely cold accretion. For massive cores (~100 Earth masses), the post-formation luminosities of core accretion planets become so high that they approach those in the hot start scenario that is often associated with gravitational instability. For the mechanism to work, it is necessary that the solids are accreted before or during gas runaway accretion and that they sink during this time deep into the planet.

Conclusions. We make no claims about whether such massive cores can actually form in giant planets especially at large orbital distances. But if they can form, it becomes difficult to rule out core accretion as the formation mechanism based solely on luminosity for directly imaged planets that are more luminous than predicted for low core masses. Instead of invoking gravitational instability as the consequently necessary formation mode, the high luminosity can also be caused, at least in principle, simply by a more massive core.