The Effect of the Chromospheric Temperature on Coronal Heating

TL;DR

This study uses MHD simulations to explore how variations in chromospheric temperature influence the structure and heating of the solar corona, revealing that higher chromospheric temperatures can inhibit coronal formation especially in shorter loops.

Contribution

The paper introduces a simplified model linking chromospheric temperature to coronal loop length and magnetic field strength, providing a new condition for coronal formation based on these parameters.

Findings

Hotter chromospheres extend higher, shortening coronal loops and increasing conductive cooling.

A derived condition for coronal formation depends on loop length, chromospheric temperature, and magnetic field strength.

Enhanced chromospheric heating can prevent the development of a hot corona in certain conditions.

Abstract

Recent observational and numerical studies show a variety of thermal structures in the solar chromosphere. Given that the thermal interplay across the transition region is a key to coronal heating, it is worth investigating how different thermal structures of the chromosphere yield different coronal properties. In this work, by MHD simulations of Alfv\'{e}n-wave heating of coronal loops, we study how the coronal properties are affected by the chromospheric temperature. To this end, instead of solving the radiative transfer equation, we employ a simple radiative loss function so that the chromospheric temperature is easily tuned. When the chromosphere is hotter, because the chromosphere extends to a larger height, the coronal part of the magnetic loop becomes shorter, which enhances the conductive cooling. A larger loop length is therefore required to maintain the high-temperature corona against the thermal conduction. From our numerical simulations we derive a condition for the coronal formation with respect to the half loop length $l_{\rm loop}$ in a simple form: $l_{\rm loop} > a T_{\rm min} + l_{\rm th}$, where $T_{\rm min}$ is the minimum temperature in the atmosphere and parameters $a$ and $l_{\rm th}$ have negative dependencies on the coronal field strength. Our conclusion is that the chromospheric temperature has a non-negligible impact on coronal heating for loops with small length and weak coronal field. In particular, the enhanced chromospheric heating could prevent the formation of the corona.