Coronal Heating Law Constrained by Microwave Gyroresonant Emission

The question why the solar corona is much hotter than the visible solar surface still puzzles solar researchers. Most theories of the coronal heating involve a tight coupling between the coronal magnetic field and the associated thermal structure. This coupling is based on two facts: (i) the magnetic field is the main source of the energy in the corona and (ii) the heat transfer preferentially happens along the magnetic field, while is suppressed across it. However, most of the information about the coronal heating is derived from the analysis of extreme ultraviolet or soft X-ray emissions, which are not explicitly sensitive to the magnetic field. This paper employs another electromagnetic channel - the sunspot-associated microwave gyroresonant emission, which is explicitly sensitive to both the magnetic field and thermal plasma. We use nonlinear force-free field reconstructions of the magnetic skeleton dressed with a thermal structure as prescribed by a field-aligned hydrodynamics to constrain the coronal heating model. We demonstrate that the microwave gyroresonant emission is extraordinarily sensitive to details of the coronal heating. We infer heating model parameters consistent with observations.