Planetary Population Synthesis Coupled With Atmospheric Escape: A Statistical View of Evaporation

Abstract

We apply hydrodynamic evaporation models to different synthetic planet populations that were obtained from a planet formation code based on a core-accretion paradigm. We investigated the evolution of the planet populations using several evaporation models, which are distinguished by the driving force of the escape flow (X-ray or EUV), the heating efficiency in energy-limited evaporation regimes, or both. Although the mass distribution of the planet populations is barely affected by evaporation, the radius distribution clearly shows a break at approximately 2 R ⊕ . We find that evaporation can lead to a bimodal distribution of planetary sizes (Owen & Wu 2013) and to an "evaporation valley" running diagonally downwards in the orbital distance -planetary radius plane, separating bare cores from low-mass planet that have kept some primordial H/He. Furthermore, this bimodal distribution is related to the initial characteristics of the planetary populations because lowmass planetary cores can only accrete small primordial H/He envelopes and their envelope masses are proportional to their core masses. We also find that the population-wide effect of evaporation is not sensitive to the heating efficiency of energy-limited description. However, in two extreme cases, namely without evaporation or with a 100% heating efficiency in an evaporation model, the final size distributions show significant differences; these two scenarios can be ruled out from the size distribution of Kepler candidates.

Radiative braking in the extended exosphere of GJ 436 b

“…The impact of this phenomenon on the formation and the evolution of planets has been studied through energy diagrams (Lecavelier des Etangs 2007; Ehrenreich & Désert 2011;Lammer et al 2009) and theoretical modeling applied to specific systems (e.g., Lopez et al 2012;Lopez & Fortney 2013) or populations of exoplanets (e.g., Jin et al 2014;Kurokawa & Nakamoto 2014). While massive gaseous giants like HD 209458b or HD 189733 b are subjected to moderate escape rate, leading to the loss of a few percentage points of the planet mass over the lifetime of the system, low-density planets like mini-Neptunes or super-Earths with a large volatile envelope may be significantly eroded by evaporation.…”

Characterization of exoplanets from their formation

“…In the convective regions standard zeroentropy gradient convection is assumed. Deuterium burning is included (Mollière & Mordasini 2012) while atmospheric evaporation is neglected as we are interested in massive planets which are mostly unaffected by this process (Jin et al 2014). The most important settings and parameters of the formation and evolution model can be found in Table 1.…”

Two empirical regimes of the planetary mass-radius relation

“…The formation model includes the effect of type I and II orbital migration. During the evolutionary phase, no mechanisms that can lead to inflation of the planetary radius (bloating) are included, whereas the effect of atmospheric escape is considered as described in Jin et al (2014). The planetary opacity used in the formation models is the combination of the interstellar medium (ISM) opacities (Bell & Lin 1994) reduced by a factor 0.003 plus the grain-free opacities of Freedman et al (2014).…”