The observable properties of cool winds from galaxies, AGN, and star clusters - I. Theoretical framework

Winds arising from galaxies, star clusters, and active galactic nuclei are crucial players in star and galaxy formation, but it has proven remarkably difficult to use observations of them to determine physical properties of interest, particularly mass fluxes. Much of the difficulty stems from a lack of a theory that links a physically realistic model for winds' density, velocity and covering factors to calculations of light emission and absorption. In this paper we provide such a model. We consider a wind launched from a turbulent region with a range of column densities, derive the differential acceleration of gas as a function of column density, and use this result to compute winds' absorption profiles, emission profiles and emission intensity maps in both optically thin and optically thick species. The model is sufficiently simple that all required computations can be done analytically up to straightforward numerical integrals, rendering it suitable for the problem of deriving physical parameters by fitting models to observed data. We show that our model produces realistic absorption and emission profiles for some example cases, and argue that the most promising methods of deducing mass fluxes are based on combinations of absorption lines of different optical depths, or on combining absorption with measurements of molecular line emission. In the second paper in this series, we expand on these ideas by introducing a set of observational diagnostics that are significantly more robust than those commonly in use, and that can be used to obtain improved estimates of wind properties.