K. D. Gorbunova, N. V. Erkaev

Institute of Computational Modelling, Siberian Branch of Russian Academy of Science (Krasnoyarsk, Russian Federation)

Abstract. The article considers a two-dimensional problem of hydrodynamic escape of the planet’s primordial hydrogen atmosphere as a result of absorption of extreme ultraviolet (EUV) radiation from its host star. As a test case, the model is applied using the parameters of a recently discovered exoplanet TOI-421b, which, according to accepted classification, belongs to so-called class of ``warm mini-Neptunes''. The hydrodynamic parameters are determined by solving the non-stationary Euler and entropy production equations in a spherical coordinate system. The EUV intensity is calculated using the radiation transport equation along parallel rays, with an absorption coefficient proportional to the density of the hydrogen atoms. The numerical method is based on a finite-difference scheme of the modified MacCormack --- Runge--Kutta type on a spherical grid with a nonuniform step along the radial direction and a constant step along the spherical angle. The calculation of the radiation intensity at the grid points is perfomed along the characteristics with density interpolation. Steady-state two-dimensional profiles of physical parameters in the upper atmosphere obtained as the result of calculations are presented. An estimate of the dayside atmospheric mass-loss rate and the rate of mass transfer to the nightside under constant external conditions is provided.

Key Words: mathematical modelling, exoplanet, upper atmospheres, two-dimensional problem, atmospheric escape

For citation: K. D. Gorbunova, N. V. Erkaev. 2D model of the hydrodynamic escape of planetary atmospheres. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 27:4(2025), 500–516. DOI: https://doi.org/10.15507/2079-6900.27.202504.500-516

Information about the authors:

Kseniia D. Gorbunova, Engineer, Department of Computational Physics, Institute of Computational Modelling, Siberian Branch of Russian Academy of Science (50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation), ORCID: http://orcid.org/0009- 0000-7593-3874, gorbunova.kd@icm.krasn.ru

Nikolay V. Erkaev, Dr.Sci. (Phys. and Math.), Chief researcher, Institute of Computational Modelling, Siberian Branch of Russian Academy of Science (50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation), ORCID: http://orcid.org/0000- 0001-8993-6400, erkaev@icm.krasn.ru