Stratification of canopy magnetic fields in a plage region. Constraints\n from a spatially-regularized weak-field approximation method

Abstract

The role of magnetic fields in the chromospheric heating problem remains\ngreatly unconstrained. Most theoretical predictions from numerical models rely\non a magnetic configuration, field strength and connectivity whose details have\nnot been well established with observational studies. High-resolution studies\nof chromospheric magnetic fields in plage are very scarce or non-existent in\ngeneral. Our aim is to study the stratification of the magnetic field vector in\nplage regions. We use high-spatial resolution full-Stokes observations acquired\nwith CRISP instrument at the Swedish 1-m Solar Telescope in the Mg I\n$\\lambda$5173, Na I $\\lambda$5896 and Ca II $\\lambda$8542 lines. We have\ndeveloped a spatially-regularized weak-field approximation (WFA) method based\non the idea of spatial regularization. This method allows for a fast\ncomputation of magnetic field maps for an extended field of view. The fidelity\nof this new technique has been assessed using a snapshot from a realistic 3D\nmagnetohydrodynamics simulation. We have derived the depth-stratification of\nthe line-of-sight component of the magnetic field from the photosphere to the\nchromosphere in a plage region. The magnetic fields are concentrated in the\nintergranular lanes in the photosphere and expand horizontally toward the\nchromosphere, filling all the space and forming a canopy. Our results suggest\nthat the lower boundary of this canopy must be located around 400-600 km from\nthe photosphere. The mean canopy total magnetic field strength in the lower\nchromosphere ($z\\approx760$ km) is 658 G. At $z=1160$ km we estimate\n$<B_\\parallel>\\approx 417$ G. We propose a modification to the WFA that\nimproves its applicability to data with worse signal-to-noise ratio. These\nmethods provide a quick and reliable way of studying multi-layer magnetic field\nobservations without the many difficulties inherent to other inversion methods.\n