Corona and XUV emission modelling of the Sun and Sun-like stars

¹ National Astronomical Observatory of Japan, National Institutes of Natural Sciences, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan
e-mail: munehito.shoda@nao.ac.jp
² Department of Earth and Space Science, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan

Received: 16 June 2021
Accepted: 6 September 2021

Abstract

The X-ray and extreme-ultraviolet (EUV) emissions from low-mass stars significantly affect the evolution of the planetary atmosphere. However, it is observationally difficult to constrain the stellar high-energy emission because of the strong interstellar extinction of EUV photons. In this study, we simulate the XUV (X-ray plus EUV) emission from Sun-like stars by extending the solar coronal heating model that self-consistently solves, with sufficiently high resolution, the surface-to-coronal energy transport, turbulent coronal heating, and coronal thermal response by conduction and radiation. The simulations are performed with a range of loop lengths and magnetic filling factors at the stellar surface. With the solar parameters, the model reproduces the observed solar XUV spectrum below the Lyman edge, thus validating its capability of predicting the XUV spectra of other Sun-like stars. The model also reproduces the observed nearly linear relation between the unsigned magnetic flux and the X-ray luminosity. From the simulation runs with various loop lengths and filling factors, we also find a scaling relation, namely log L_EUV = 9.93 + 0.67 log L_X, where L_EUV and L_X are the luminosity in the EUV (100 Å < λ ≤ 912 Å) and X-ray (5 Å < λ ≤ 100 Å) range, respectively, in cgs. By assuming a power–law relation between the Rossby number and the magnetic filling factor, we reproduce the renowned relation between the Rossby number and the X-ray luminosity. We also propose an analytical description of the energy injected into the corona, which, in combination with the conventional Rosner–Tucker–Vaiana scaling law, semi-analytically explains the simulation results. This study refines the concepts of solar and stellar coronal heating and derives a theoretical relation for estimating the hidden stellar EUV luminosity from X-ray observations.