Radiative cooling of swept up gas in AGN-driven galactic winds and its implications for molecular outflows

We recently used hydro-chemical simulations to demonstrate that molecular outflows observed in luminous quasars can be explained by molecule formation within the AGN wind. However, these simulations cover a limited parameter space, due to their computational cost. We have therefore developed an analytic model to follow cooling in the shocked ISM layer of an AGN wind. We explore different ambient densities ($1-10^{4} \, \rm{cm}^{-3}$), density profile slopes ($0-1.5$), AGN luminosities ($10^{44}-10^{47} \, \rm{erg} \, \rm{s}^{-1}$), and metallicities ($0.1-3 \rm{Z}_{\odot}$). The swept up gas mostly cools within ~1 Myr. Based on our previous simulations, we predict that this gas would produce observable molecular outflows. The instantaneous momentum boost initially increases as the outflow decelerates. However, it reaches a maximum of $\approx$20, due to work done against the gravitational potential. The predicted time-averaged observational estimate of the molecular outflow momentum boost reaches a maximum of $\approx1-2$, partly due to our assumed molecular fraction, 0.2, but also because the instantaneous and observational, time-averaged definitions are not equivalent. Thus recent observational estimates of order unity momentum boosts do not necessarily rule out energy-driven outflows. Finally, we find that dust grains are likely to re-form by accretion of metals after the shocked ISM layer has cooled, assuming that a small fraction of dust grains swept up after this layer has cooled are able to mix into the cool phase, and assuming that grain growth remains efficient in the presence of the strong AGN radiation field. This would enable rapid molecule formation, as assumed in our models.