The Physics of Galactic Winds Driven by Cosmic Rays I: Diffusion

The physics of Cosmic ray (CR) transport remains a key uncertainty in assessing whether CRs can produce galaxy-scale outflows consistent with observations. In this paper, we elucidate the physics of CR-driven galactic winds for CR transport dominated by diffusion. A companion paper considers CR streaming. We use analytic estimates validated by time-dependent spherically-symmetric simulations to derive expressions for the mass-loss rate, momentum flux, and speed of CR-driven galactic winds, suitable for cosmological-scale or semi-analytic models of galaxy formation. For CR diffusion coefficients $\kappa \gtrsim r_0 c_i$ where $r_0$ is the base radius of the wind and $c_i$ is the isothermal gas sound speed, the asymptotic wind energy flux is comparable to that supplied to CRs, and the outflow rapidly accelerates to supersonic speeds. By contrast, for $\kappa \lesssim r_0 c_i$, CR-driven winds accelerate more slowly and lose most of their energy to gravity, a CR analogue of photon-tired stellar winds. Given CR diffusion coefficients estimated using Fermi gamma-ray observations of pion decay, we predict mass-loss rates in CR-driven galactic winds of order the star formation rate for dwarf and disc galaxies. The dwarf galaxy mass-loss rates are small compared to the mass-loadings needed to reconcile the stellar and dark matter halo mass functions. For nuclear starbursts (e.g., M82, Arp 220), CR diffusion and pion losses suppress the CR pressure in the galaxy and the strength of CR-driven winds. We discuss the implications of our results for interpreting observations of galactic winds and for the role of CRs in galaxy formation.