EUV-driven mass-loss of protoplanetary cores with hydrogen-dominated atmospheres: the influences of ionization and orbital distance

Abstract

We investigate the loss rates of the hydrogen atmospheres of terrestrial planets with a range of masses and orbital distances by assuming a stellar extreme ultraviolet (EUV) luminosity that is 100 times stronger than that of the current Sun. We apply a 1D upper atmosphere radiation absorption and hydrodynamic escape model that takes into account ionization, dissociation and recombination to calculate hydrogen mass loss rates. We study the effects of the ionization, dissociation and recombination on the thermal mass loss rates of hydrogen-dominated super-Earths and compare the results to those obtained by the energy-limited escape formula which is widely used for mass loss evolution studies. Our results indicate that the energy-limited formula can to a great extent over-or underestimate the hydrogen mass loss rates by amounts that depend on the stellar EUV flux and planetary parameters such as mass, size, effective temperature, and EUV absorption radius.

Young planets under extreme UV irradiation

“…To model the planetary upper atmosphere and infer the mass-loss rates, we employ an updated version of the 1D hydrodynamical code described in detail in the appendix of Erkaev et al (2016). This model treats the planetary upper atmosphere as a clear hydrogen gas envelope, including the effects of recombination, dissociation, ionization of the hydrogen atoms and molecules, and Ly-α cooling.…”

“…Watson et al 1981;Yelle 2004;Murray-Clay et al 2009;Cecchi-Pestellini et al 2009;Owen & Jackson 2012;Shematovich et al 2014;Salz et al 2016). In this work, we follow the considerations of Erkaev et al (2016) and adopt a value of 15%, based on the results of the direct simulation Monte Carlo model calculations of Shematovich et al (2014), which model photolytic and electron impact processes in the thermosphere by solving the kinetic Boltzmann equation.…”

“…In the absence of a measured stellar XUV spectrum and to speed up computations for the XUV stellar flux absorption, we follow the approach of Erkaev et al (2016), who considered that the whole stellar EUV flux is emitted at a single wavelength of 60 nm, which corresponds to the position of the peak of the stellar EUV emission. To account for X-ray heating, we additionally consider absorption of stellar X-ray photons by the planetary atmosphere.…”

“…One dimensional models are widely used for exoplanet studies, particularly with respect to upper atmosphere modelling (see e.g. Murray-Clay et al 2009;Shaikhislamov et al 2014;Salz et al 2016;Erkaev et al 2016Erkaev et al , 2017Fossati et al 2017;Lammer et al 2016). An upgrade to 2D or 3D simulations is instead required to model the interaction between the expanding planetary atmosphere with the stellar wind, particularly when considering ion pick-up processes related to planetary atmospheric escape.…”

Effect of stellar wind induced magnetic fields on planetary obstacles of non-magnetized hot Jupiters

“…To study the EUV heating and expansion and to infer the mass-loss rates of the hydrogen-dominated upper atmosphere of the planet, we apply a time-dependent 1D hydrodynamic model described in detail by Erkaev et al (2016). The model solves the absorption of the stellar EUV flux by the thermosphere, the hydrodynamic equations for mass, momentum, and energy conservation, and the continuity equations for neutrals and ions (both atoms and molecules).…”