Heating of the solar chromosphere through current dissipation

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