Approximations for radiative cooling and heating in the solar chromosphere

TL;DR

This paper develops empirical formulas to approximate radiative cooling and heating in the solar chromosphere, enabling more efficient simulations by simplifying complex radiative transfer calculations.

Contribution

It introduces simple, empirically derived recipes for radiative energy balance in key chromospheric lines, based on detailed 2D MHD simulations.

Findings

Formulas for radiative cooling in hydrogen, calcium, and magnesium lines.

Formulas for radiative heating in cool chromospheric pockets.

A recipe for chromospheric heating from coronal radiation.

Abstract

Context. The radiative energy balance in the solar chromosphere is dominated by strong spectral lines that are formed out of LTE. It is computationally prohibitive to solve the full equations of radiative transfer and statistical equilibrium in 3D time dependent MHD simulations. Aims. To find simple recipes to compute the radiative energy balance in the dominant lines under solar chromospheric conditions. Methods. We use detailed calculations in time-dependent and 2D MHD snapshots to derive empirical formulae for the radiative cooling and heating. Results. The radiative cooling in neutral hydrogen lines and the Lyman continuum, the H and K and intrared triplet lines of singly ionized calcium and the h and k lines of singly ionized magnesium can be written as a product of an optically thin emission (dependent on temperature), an escape probability (dependent on column mass) and an ionization fraction (dependent on temperature). In the cool pockets of the chromosphere the same transitions contribute to the heating of the gas and similar formulae can be derived for these processes. We finally derive a simple recipe for the radiative heating of the chromosphere from incoming coronal radiation. We compare our recipes with the detailed results and comment on the accuracy and applicability of the recipes.