Approximate Calculation of the Thermal Loss of the Atmosphere of a Hot Exoplanet in a Low Orbit with Taking into Account the Ellipticity

Abstract

The paper presents the results of calculations using an approximate approach to estimating the thermal loss of the atmosphere of a hot exoplanet. The objective of simulation was to study a system of a yellow dwarf of the spectral type G with an exoplanet like a hot sub-Neptune or super-Earth. Estimates of the atmospheric loss rate for a hot sub-Neptune in weakly and strongly elliptical orbits are obtained. Calculations have shown that the atmospheric loss $\dot{M}_{T}$ averaged over the orbital period of the model hot sub-Neptune varies from $5.8\times 10^{17}$ g for an orbit with $e=0.0$ to $2.6\times 10^{18}$ g for an orbit with $e=0.8$, that is, it increases by almost 4.5 times. Moreover, for $e=0.2,0.4,$ and $0.6$ the values of $\dot{M}_{T}$ are equal to $6.3\times 10^{17}$ g, $7.6\times 10^{17}$ g, and $1.2\times 10^{18}$ g respectively. Using the average atmospheric mass loss per orbit, we can approximately estimate the time of total atmospheric escape of the considered sub-Neptune—at $e=0.0$, this time is approximately equal to 0.32 billion years, and at $e=0.8$—approximately 0.07 billion years. Accordingly, we can conclude that the initial ellipticity of the hot exoplanet’s orbit is an important factor in estimating the loss rate of the primary hydrogen-helium atmosphere for sub-Neptunes and super-Earths.