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 cosmic-ray heating at the cloud edge strongly reshapes the local temperature and pressure structure. When cosmic rays dominate the energy budget in this boundary layer, thermal conduction becomes essential to carry away excess heat and maintain a steady state. The resulting transition region is broader and shows internal substructure, with distinct zones where heating, cooling, and conduction balance differently. These structured layers naturally produce enhanced columns of warm gas traced by ions such as 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.