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We recently used hydro-chemical simulations to demonstrate that molecularoutflows observed in luminous quasars can be explained by molecule formationwithin the AGN wind. However, these simulations cover a limited parameterspace, due to their computational cost. We have therefore developed an analyticmodel to follow cooling in the shocked ISM layer of an AGN wind. We exploredifferent ambient densities ($1-10^{4} \, \rm{cm}^{-3}$), density profileslopes ($0-1.5$), AGN luminosities ($10^{44}-10^{47} \, \rm{erg} \,\rm{s}^{-1}$), and metallicities ($0.1-3 \rm{Z}_{\odot}$). The swept up gasmostly cools within ~1 Myr. Based on our previous simulations, we predict thatthis gas would produce observable molecular outflows. The instantaneousmomentum boost initially increases as the outflow decelerates. However, itreaches a maximum of $\approx$20, due to work done against the gravitationalpotential. The predicted time-averaged observational estimate of the molecularoutflow momentum boost reaches a maximum of $\approx1-2$, partly due to ourassumed molecular fraction, 0.2, but also because the instantaneous andobservational, time-averaged definitions are not equivalent. Thus recentobservational estimates of order unity momentum boosts do not necessarily ruleout energy-driven outflows. Finally, we find that dust grains are likely tore-form by accretion of metals after the shocked ISM layer has cooled, assumingthat a small fraction of dust grains swept up after this layer has cooled areable to mix into the cool phase, and assuming that grain growth remainsefficient in the presence of the strong AGN radiation field. This would enablerapid molecule formation, as assumed in our models.

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