The code used to solve the equations and generate plots is available here.

In this paper, we model cosmic-ray mediated thermal fronts that form between warm ($10^4$ K) and hot ($10^6$ K) phases of the circumgalactic medium (CGM). These 1D steady-state solutions self-consistently include CR heating, thermal conduction, radiative cooling, and gas flow.

A central finding is that CR heating, especially near cloud interfaces, strongly reshapes the temperature and pressure profiles across the front. When CRs dominate the energy budget near the cloud edge, thermal conduction becomes essential to carry away excess energy and maintain a steady state. The resulting fronts are broader and more structured than classical conductive interfaces, with enhanced columns of intermediate ions like O VI and N V.

We distinguish between static and evaporative fronts and examine the interplay between enthalpy flux, conduction, and CR heating. Diagnostic line ratios (e.g., Si IV/C IV, C IV/O VI, N V/O VI) are computed across the models and compared to absorption-line data from Wakker et al. (2012). We find that magnetic field strength and CR pressure critically shape the front structure and influence the predicted observables.

More broadly, our results suggest that cosmic rays can play an active role in setting the thermal and ionization structure of the warm-hot CGM, and may leave observable spectral signatures not captured by classical cooling-conduction models.