Cosmic Ray Heating of the Early IGM: Realistic Galaxy Populations, Reduced Efficiency, and 21-cm Signatures

Abstract

Cosmic rays (CRs) accelerated by the first supernovae could heat the intergalactic medium (IGM) before reionization. Previous 21-cm simulations, assuming a kinetic-energy power-law spectrum and simplified galaxy populations, found that CR heating can rival X-ray heating from high-mass X-ray binaries, imprint a distinct signature on the 21-cm power spectrum, and flatten the absorption trough of the global 21-cm signal. Here we model CR heating in 21cmFAST with: (i) the momentum power-law spectrum predicted by diffusive shock acceleration; (ii) Coulomb losses off free electrons; and (iii) injection from data-informed populations of atomic-cooling and molecularly cooled galaxies. We find that CR heating is about an order of magnitude weaker than previously estimated because a momentum power law places little energy in the sub-relativistic protons ($\lesssim 40$ MeV) that supply 99% of the heat. For our fiducial spectral slope, at the hard end of those inferred for Galactic supernova remnants, and for matched efficiency, this reduces the heating by a factor of $\approx 12$, and together with a more realistic galaxy model, by a factor of $\approx 28$ at $z = 15$. At the efficiencies that supernovae can supply, CR heating is weaker than standard X-ray heating, and the global signal alone cannot tell the two apart. Distinguishing CR from X-ray heating with the 21-cm power spectrum requires CR efficiencies a few times higher than those expected from local observations. At such efficiencies, CR heating yields up to $\approx 55\%$ more power than X-ray heating at matched global signal (median over scales), compared with only 3-6% at a locally motivated efficiency. A flattened absorption trough, like the one claimed by EDGES, requires efficiencies over two orders of magnitude above the local ones, beyond plausible Population III supernova budgets.