Heating of the solar chromosphere through current dissipation

J. M. da Silva Santos, S. Danilovic, J. Leenaarts, J. de la Cruz Rodríguez, X. Zhu, S. M. White, G. J. M. Vissers, M. Rempel

Published 2022-02-08Version 1

The solar chromosphere is heated to temperatures higher than predicted by radiative equilibrium. This excess heating is larger in active regions where the magnetic field is stronger. We aim to investigate the magnetic topology associated to an area of enhanced millimeter (mm) brightness temperatures in a solar active region mapped by the Atacama Large Millimeter/submillimeter Array (ALMA) using spectropolarimetric coobservations with the 1-m Swedish Solar Telescope (SST). We use Milne-Eddington inversions, nonlocal thermodynamic equilibrium (non-LTE) inversions, and a magnetohydrostatic extrapolation to obtain constraints on the three-dimensional stratification of temperature, magnetic field, and radiative energy losses. We compare the observations to a snapshot of a magnetohydrodynamics simulation and investigate the formation of the thermal continuum at 3 mm using contribution functions. We find enhanced heating rates in the upper chromosphere of up to $\sim 5\rm\,kW\,m^{-2}$ where small-scale emerging loops interact with the overlying magnetic canopy leading to current sheets as shown by the magnetic field extrapolation. Our estimates are about a factor of two higher than canonical values, but they are limited by the ALMA spatial resolution ($\sim 1.2^{\prime\prime}$). Band 3 brightness temperatures reach about $\sim10^{4}\,$K in the region, and the transverse magnetic field strength inferred from the non-LTE inversions is of the order of $\sim 500\,$G in the chromosphere. We quantitatively reproduce many of the observed features including the integrated radiative losses in our numerical simulation, and we conclude that the heating is caused by dissipation in current sheets. However, the simulation shows a complex stratification in the flux emergence region where distinct layers may contribute significantly to the emission in the mm continuum.