Coronal heating driven by spatially sparse and temporalintermittent energy release: a kinetic approach

Aims

We aim to investigate how the combined effects of spatial sparsity and temporal intermittency of stochastic heating events shape the stationary density and temperature profiles of the coronal plasma. We also aim to establish a theoretical kinetic framework capable of linking coronal heating with EUV observations.

Methods

We extend the kinetic model of Barbieri et al. (2025) by introducing a time-dependent stochastic boundary condition that accounts for intermittent heating at the chromospheric base. A surface coarse-graining procedure is applied to derive Vlasov-type equations for the averaged distribution functions. Analytical expressions are obtained for the corresponding density, temperature, and Differential Emission Measure (DEM) profiles, valid in the regime where the heating time scales are much shorter than the electron crossing time.

Results

We show that the temperature inversion and the coronal temperature plateau arise naturally when the combined parameter A = A_S × A_t is much smaller than unity, where A_S is the surface filling factor of heating events and A_t is their temporal duty cycle. Spatial and temporal intermittency are found to contribute in the same way to shaping the density and temperature profiles. The computed DEM exhibits a monotonic decrease with temperature up to 10⁶ K, followed by a peak marking the transition to the low corona, and shows good agreement with the observational results reported by Dolliou et al. (2024).

Conclusions

The present model unifies previous spatial and temporal kinetic descriptions of coronal heating within a single analytical framework. It provides a direct connection between the microscopic dynamics of stochastic heating and observable quantities such as the DEM.