The Planetary Accretion Shock. II. Grid of Postshock Entropies and Radiative Shock Efficiencies for Nonequilibrium Radiation Transport

Abstract

In the core-accretion formation scenario of gas giants, most of the gas accreting onto a planet is processed through an accretion shock. In this series of papers we study this shock since it is key in setting the forming planet's structure and thus its post-formation luminosity, with dramatic observational consequences. We perform one-dimensional grey radiation-hydrodynamical simulations with non-equilibrium (two-temperature) radiation transport and up-to-date opacities. We survey the parameter space of accretion rate, planet mass, and planet radius and obtain post-shock temperatures, pressures, and entropies, as well as global radiation efficiencies. We find that usually, the shock temperature T shock is given by the "free-streaming" limit. At low temperatures the dust opacity can make the shock hotter but not significantly. We corroborate this with an original semi-analytical derivation of T shock . We also estimate the change in luminosity between the shock and the nebula. Neither T shock nor the luminosity profile depend directly on the optical depth between the shock and the nebula. Rather, T shock depends on the immediate pre-shock opacity, and the luminosity change on the equation of state (EOS). We find quite high immediate post-shock entropies (S ≈ 13-20 k B m H −1 ), which makes it seem unlikely that the shock can cool the planet. The global radiation efficiencies are high (η phys 97 %) but the remainder of the total incoming energy, which is brought into the planet, exceeds the internal luminosity of classical cold starts by orders of magnitude. Overall, these findings suggest that warm or hot starts are more plausible.

The endgame of gas giant formation: accretion luminosity and contraction post-runaway

“…The evolution during and prior to runaway is otherwise identical between the two tracks, as is the treatment of the accretion shock, which we do not take to be isothermal with the nebula, but which instead thermalizes at the blackbody temperature. In this sense, our calculations are compatible with 'hot start' models for post-formation cooling (see Marleau et al 2017 andMarleau et al 2019 for details).…”

Planet formation around M dwarfs via disc instability

“…Marley et al 2007;Mordasini et al 2012;Mordasini 2013;Baruteau et al 2016). The estimated temperatures are similar to the temperatures of the accretion shock around planets formed by core accretion (Marleau et al 2017(Marleau et al , 2019Szulágyi 2017;Szulágyi et al 2018;Szulágyi & Mordasini 2017) and therefore their circumplanetary discs are also expected to be relatively hot. These high temperatures contradict the results of the disc instability model presented in , as in the simulations presented here we were able to follow the collapse of a fragment at much higher densities and capture the formation of the first and second core.…”

“…Nevertheless, most of the exoplanets undergo the second collapse phase and therefore attain high central temperatures (6000-12 000 K). These temperatures are similar to the temperatures at the accretion shocks around planets formed by core accretion Marleau et al 2019), therefore the temperature alone cannot provide a way to distinguish between these two formation scenarios.…”

Retrieving scattering clouds and disequilibrium chemistry in the atmosphere of HR 8799e

“…It was found by Spiegel & Burrows (2012); Marley et al (2012); Marleau & Cumming (2014), however, that at least a classical cold start assumption (Marley et al 2007) is ruled out for these planets. In any case, recent theoretical modeling of the physics of the accretion shock (Marleau et al 2017(Marleau et al , 2019 and of the structure of accreting planets Cumming et al 2018)…”