Kinetic collisionless model of the solar transition region and corona with spatially intermittent heating

LIRA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris-Cité, Meudon, France

^⋆ Corresponding author: luca.barbieri@obspm.fr

Received: 22 September 2025
Accepted: 31 October 2025

Abstract

Context. The solar corona exhibits a striking temperature inversion, with plasma temperatures exceeding 10⁶ K above a much cooler chromosphere. How the coronal plasma reaches such extreme temperatures remains a fundamental open question in solar and plasma physics, known as the coronal heating problem.

Aims. We investigate whether localized heating events, spatially distributed across the upper chromosphere and base of the transition region, combined with a collisionless corona, can self-consistently generate realistic temperature and density profiles without requiring direct energy deposition within the corona itself.

Models. We develop a 3D kinetic model of a collisionless stellar atmosphere embedded in a uniform magnetic field, where heating occurs intermittently at the chromosphere–transition region interface. A surface coarse-graining procedure is introduced to capture the spatial intermittency of heating, leading to non-thermal boundary conditions for the Vlasov equation. We derive analytical expressions for the stationary distribution functions and compute the corresponding macroscopic profiles.

Results. We show that spatially intermittent heating, when coarse-grained over a surface containing many localized events, produces suprathermal particle distributions and a temperature inversion via velocity filtration. The resulting density and temperature profiles feature a transition region followed by a hot corona, provided that heating events are spatially sparse, consistently with solar observations. This result holds independently of the specific statistical distribution of temperature increments. Importantly, no local heating is applied within the corona.

Conclusions. The model demonstrates that spatial intermittency alone, i.e. a sparse distribution of heated regions at the chromospheric interface, is sufficient to explain the formation of the transition region and the high-temperature corona.