Stratification of canopy magnetic fields in a plage region

Context. The role of magnetic fields in the chromospheric heating problem remains greatly unconstrained. Most theoretical predictions from numerical models rely on a magnetic configuration, field strength, and connectivity; the details of which have not been well established with observational studies for many chromospheric scenarios. High-resolution studies of chromospheric magnetic fields in plage are very scarce or non existent in general. Aims. Our aim is to study the stratification of the magnetic field vector in plage regions. Previous studies predict the presence of a magnetic canopy in the chromosphere that has not yet been studied with full-Stokes observations. We use high-spatial resolution full-Stokes observations acquired with the CRisp Imaging Spectro-Polarimeter (CRISP) at the Swedish 1-m Solar Telescope in the Mg I 5173 Å, Na I 5896 Å and Ca II 8542 Å lines. Methods. We have developed a spatially-regularized weak-field approximation (WFA) method, based on the idea of spatial regularization. This method allows for a fast computation of magnetic field maps for an extended field of view. The fidelity of this new technique has been assessed using a snapshot from a realistic 3D magnetohydrodynamics simulation. Results. We have derived the depth-stratification of the line-of-sight component of the magnetic field from the photosphere to the chromosphere in a plage region. The magnetic fields are concentrated in the intergranular lanes in the photosphere and expand horizontally toward the chromosphere, filling all the space and forming a canopy. Our results suggest that the lower boundary of this canopy must be located around 400 − 600 km from the photosphere. The mean canopy total magnetic field strength in the lower chromosphere (z ≈ 760 km) is 658 G. At z = 1160 km, we estimate ⟨B∥⟩ ≈ 417 G. Conclusions. In this study we propose a modification to the WFA that improves its applicability to data with a worse signal-to-noise ratio. We have used this technique to study the magnetic properties of the hot chromospheric canopy that is observed in plage regions. The methods described in this paper provide a quick and reliable way of studying multi layer magnetic field observations without the many difficulties inherent to other inversion methods.