Inference of the chromospheric magnetic field configuration of solar plage using the Ca II 8542 {\AA} line.

Context: It has so far proven impossible to reproduce all aspects of the solar plage chromosphere in quasi-realistic numerical models. The magnetic field configuration in the lower atmosphere is one of the few free parameters in such simulations. The literature only offers proxy-based estimates of the field strength, as it is difficult to obtain observational constraints in this region. Sufficiently sensitive spectro-polarimetric measurements require a high signal-to-noise ratio, spectral resolution and cadence, which are at the limit of current capabilities. Aims: We use critically sampled spectro-polarimetric observations of the Ca II $\lambda$ 8542 line obtained with the CRISP instrument of the Swedish 1-m Solar Telescope, to study the strength and inclination of the chromospheric magnetic field of a plage region. This will provide direct physics-based estimates of these values, which could aid modellers to put constraints on plage models. Methods: We increased the signal-to-noise ratio of the data by applying several methods including deep learning and PCA. We reach a noise level of $6 \cdot 10^{-4} \: I_c$. We then use STiC, a non-local thermodynamic equilibrium (NLTE) inversion code to infer the atmospheric structure and magnetic field pixel by pixel. Results: We are able to infer a magnetic field strength and inclination for a plage region and for fibrils in the surrounding canopy. In the plage we report an absolute field strength of $|B|= 405 \pm 90$ G, with an inclination of $9^\circ \pm 6^\circ $ with respect to the local vertical. This value for |B| is roughly double of what was reported previously, while the inclination matches previous studies done in the photosphere. In the fibrillar region we found $|B|= 290 \pm 50$ G, with an inclination of $49^\circ \pm 16^\circ$.