Probing the blow-off criteria of hydrogen-rich ‘super-Earths’

Abstract

The discovery of transiting "super-Earths" with inflated radii and known masses such as Kepler-11b-f, GJ 1214b and 55 Cnc e, indicates that these exoplanets did not lose their nebula-captured hydrogen-rich, degassed or impact-delivered protoatmospheres by atmospheric escape processes. Because hydrodynamic blow-off of atmospheric hydrogen atoms is the most efficient atmospheric escape process we apply a time-dependent numerical algorithm which is able to solve the system of 1-D fluid equations for mass, momentum, and energy conservation to investigate the criteria under which "super-Earths" with hydrogen-dominated upper atmospheres can experience hydrodynamic expansion by heating of the stellar XUV (soft X-rays and extreme ultraviolet) radiation and thermal escape via blow-off. Depending on orbit location, XUV flux, heating efficiency and the planet's mean density our results indicate that the upper atmospheres of all "super-Earths" can expand to large distances, so that besides of Kepler-11c all of them experience atmospheric mass-loss due to Roche lobe overflow. The atmospheric mass-loss of the studied "super-Earths" is one to two orders of magnitude lower compared to that of "hot Jupiters" such as HD 209458b, so that one can expect that these exoplanets cannot lose their hydrogen-envelopes during their remaining lifetimes.

Extreme hydrodynamic atmospheric loss near the critical thermal escape regime

“…To study the XUV-heated upper atmosphere structure and thermal escape rates of exposed hydrogen atoms, we apply a 1-D hydrodynamic upper atmosphere model with an energy absorption model, that is described in detail in Erkaev et al (2013Erkaev et al ( , 2014 and Lammer et al (2013aLammer et al ( , 2014. The model solves the system of the hydrodynamic equations for mass,…”

“…γ is the polytropic index, g the gravitational acceleration and QXUV is the XUV volume heating rate (Erkaev et al 2013)…”

“…where r is the normalized radial distance r = R/R0, R0 is the lower boundary radius at the base of the thermosphere near the mesopause/homopause level, η is the heating efficiency which is typically 15% (Shematovich et al 2014), I * XUV is the XUV flux at the upper boundary, σXUV is the XUV absorption cross section in a hydrogen atmosphere (Chassefière 1996;Erkaev et al 2013;Lammer et al 2014), and J(r, θ)XUV is a dimensionless function describing the variation the XUV flux with respect to the radial distance due to the atmospheric absorption,…”

“…Studies related to hydrodynamic escape and evolution of planetary atmospheres (e.g., Sekiya et al 1980aSekiya et al , 1980bSekiya et al , 1981Watson et al 1981;Kasting & Pollack 1983;Yelle 2004;Tian et al 2005aTian et al , 2005bMurry-Clay et al 2009;Koskinen et al 2013;Erkaev et al 2013Erkaev et al , 2014Lammer et al 2013a indicate that the heating of the upper atmosphere caused by high XUV radiation and the related hydrodynamic expansion of the bulk atmosphere is important for the escape of light gases such as hydrogen from early planetary atmospheres. The hydrodynamic outflow of the atmospheric particles is somewhat similar to that of the solar wind described by the well known isothermic model of Parker (1964aParker ( , 1964b.…”

“…This XUV heating model was further extended by Erkaev et al (2013) by taking into account the angular dependence of the heating rate. Generally, the main necessary condition for hydrodynamic escape modeling is that the sonic point c 2014 RAS should be within the collision dominated atmosphere where the Knudsen number Kn is sufficiently small.…”