Spatio-temporal analysis of chromospheric heating in a plage region

Context. Our knowledge of the heating mechanisms that are at work in the chromosphere of plage regions remains highly unconstrained from observational studies. While many heating candidates have been proposed in theoretical studies, the exact contribution from each of them is still unknown. The problem is rather difficult because there is no direct way of estimating the heating terms from chromospheric observations. Aims. The purpose of our study is to estimate the chromospheric heating terms from a multi-line high-spatial-resolution plage dataset, characterize their spatio-temporal distribution and set constraints on the heating processes that are at work in the chromosphere. Methods. We used nonlocal thermodynamical equilibrium inversions in order to infer a model of the photosphere and chromosphere of a plage dataset acquired with the Swedish 1-m Solar Telescope (SST). We used this model atmosphere to calculate the chromospheric radiative losses from the main chromospheric cooler from H I, Ca II, and Mg II atoms. In this study, we approximate the chromospheric heating terms by the net radiative losses predicted by the inverted model. In order to make the analysis of time-series over a large field of view computationally tractable, we made use of a neural network which is trained from the inverted models of two non-consecutive time-steps. We have divided the chromosphere in three regions (lower, middle, and upper) and analyzed how the distribution of the radiative losses is correlated with the physical parameters of the model. Results. In the lower chromosphere, the contribution from the Ca II lines is dominant and predominantly located in the surroundings of the photospheric footpoints. In the upper chromosphere, the H I contribution is dominant. Radiative losses in the upper chromosphere form a relatively homogeneous patch that covers the entire plage region. The Mg II also peaks in the upper chromosphere. Our time analysis shows that in all pixels, the net radiative losses can be split in a periodic component with an average amplitude of amp̅Q = 7.6 kW m−2 and a static (or very slowly evolving) component with a mean value of −26.1 kW m−2. The period of the modulation present in the net radiative losses matches that of the line-of-sight velocity of the model. Conclusions. Our interpretation is that in the lower chromosphere, the radiative losses are tracing the sharp lower edge of the hot magnetic canopy that is formed above the photosphere, where the electric current is expected to be large. Therefore, Ohmic current dissipation could explain the observed distribution. In the upper chromosphere, both the magnetic field and the distribution of net radiative losses are room-filling and relatively smooth, whereas the amplitude of the periodic component is largest. Our results suggest that acoustic wave heating may be responsible for one-third of the energy deposition in the upper chromosphere, whereas other heating mechanisms must be responsible for the rest: turbulent Alfvén wave dissipation or ambipolar diffusion could be among them. Given the smooth nature of the magnetic field in the upper chromosphere, we are inclined to rule out Ohmic dissipation of current sheets in the upper chromosphere.