Heating efficiency in hydrogen-dominated upper atmospheres

Abstract

Context. The heating efficiency η hν is defined as the ratio of the net local gas-heating rate to the rate of stellar radiative energy absorption. It plays an important role in thermal-escape processes from the upper atmospheres of planets that are exposed to stellar soft X-rays and extreme ultraviolet radiation (XUV). Aims. We model the thermal-escape-related heating efficiency η hν of the stellar XUV radiation in the hydrogen-dominated upper atmosphere of the extrasolar gas giant HD 209458b. The model result is then compared with previous thermal-hydrogen-escape studies, which assumed η hν values between 10-100%. Methods. The photolytic and electron impact processes in the thermosphere were studied by solving the kinetic Boltzmann equation and applying a Direct Simulation Monte Carlo model. We calculated the energy deposition rates of the stellar XUV flux and that of the accompanying primary photoelectrons that are caused by electron impact processes in the H 2 → H transition region in the upper atmosphere. Results. The heating by XUV radiation of hydrogen-dominated upper atmospheres does not reach higher values than 20% above the main thermosphere altitude, if the participation of photoelectron impact processes is included. Conclusions. Hydrogen-escape studies from exoplanets that assume η hν values that are ≥20% probably overestimate the thermal escape or mass-loss rates, while those who assumed values that are <20% produce more realistic atmospheric-escape rates.

High-energy irradiation and mass loss rates of hot Jupiters in the solar neighborhood

“…We adopt a heating efficiency of η = 0.15, which accounts for the fraction of the radiative energy needed for ionization processes or lost through radiative cooling. This choice agrees with recent results from Shematovich et al (2014), who find η < 0.20 in the atmosphere of HD 209458 b. Furthermore, it enables a direct comparison with the mass loss rates determined by Ehrenreich & Désert (2011), who utilized the stellar rotation based method from Lecavelier des Etangs (2007) to estimate the EUV fluxes (see Sect.…”

“…Furthermore, for the heating efficiency, values ranging from 0.1 to 1.0 are used in literature (Ehrenreich & Désert 2011), although the recent study of Shematovich et al (2014) for HD 209458 b somewhat restricts this unconfined parameter. This adds to a considerable source of uncertainty in the derivation of the high-energy irradiation (see Sect.…”

Energy-limited escape revised

“…In particular, a certain fraction of the energy input is used for ionizations, and in addition, recombinations and collisional excitations cause radiative cooling that also reduces the available energy. Atmospheric material only has to escape to the Roche-lobe height, R Rl , which is accounted for by multiplying with the fractional gravitational potential energy difference, K, between the planetary surface and the Roche-lobe height (Erkaev et al 2007): (Shematovich et al 2014), but we show that heating efficiencies vary by several orders of magnitude in individual atmospheres. The second question is the unknown size of the planetary atmosphere that absorbs the XUV radiation.…”

An evaporating planet in the wind: stellar wind interactions with the radiatively braked exosphere of GJ 436 b

“…with ρ the mean density of the planet, K tide a correction factor accounting for the contribution of tidal forces to the potential energy (Erkaev et al 2007), and η the heating efficiency, which the most recent theoretical estimations estimate at between 10 and 20% (e.g., Lammer et al 2013;Shematovich et al 2014;Owen & Alvarez 2016). The total X/EUV flux per unit area at 1 au from GJ 436, measured from 0.5 nm to the Lyman-α line (included), is F X/EUV (1 au) = 2.3 ± 0.5 erg s −1 cm −2 (Table 3).…”