Nonlinear Force-Free Field Modeling of the Solar Magnetic Carpet and Comparison with SDO/HMI and Sunrise/IMaX Observations

TL;DR

This study models the solar magnetic carpet's evolution using nonlinear force-free fields derived from observations, revealing energy deposition patterns that influence coronal heating and highlighting the need for better chromospheric magnetic measurements.

Contribution

It introduces a magneto-frictional relaxation method incorporating hyperdiffusion to simulate the 3D magnetic field evolution from observational data.

Findings

Energy deposition is concentrated within 2 Mm of the photosphere.

Insufficient energy flux at the coronal base to balance radiative and conductive losses.

Better chromospheric magnetic field data is needed for understanding coronal heating.

Abstract

In the quiet solar photosphere, the mixed polarity fields form a magnetic carpet, which continuously evolves due to dynamical interaction between the convective motions and magnetic field. This interplay is a viable source to heat the solar atmosphere. In this work, we used the line-of-sight (LOS) magnetograms obtained from the Helioseismic and Magnetic Imager (HMI) on the \textit{Solar Dynamics Observatory} (\textit{SDO}), and the Imaging Magnetograph eXperiment (IMaX) instrument on the \textit{Sunrise} balloon-borne observatory, as time dependent lower boundary conditions, to study the evolution of the coronal magnetic field. We use a magneto-frictional relaxation method, including hyperdiffusion, to produce time series of three-dimensional (3D) nonlinear force-free fields from a sequence of photospheric LOS magnetograms. Vertical flows are added up to a height of 0.7 Mm in the modeling to simulate the non-force-freeness at the photosphere-chromosphere layers. Among the derived quantities, we study the spatial and temporal variations of the energy dissipation rate, and energy flux. Our results show that the energy deposited in the solar atmosphere is concentrated within 2 Mm of the photosphere and there is not sufficient energy flux at the base of the corona to cover radiative and conductive losses. Possible reasons and implications are discussed. Better observational constraints of the magnetic field in the chromosphere are crucial to understand the role of the magnetic carpet in coronal heating.