Star formation in X-ray cluster cooling flows

Abstract

The basic equations for X-ray cluster cooling flows, including the effects of star formation, are derived. It is confirmed that cooling flows are thermally unstable, and it is found that the fastest-growing linear perturbations in the flow are radial, comoving, and isobaric. A local approximation for the star formation rate is developed which allows analytic solutions to be found for both isobaric and gravity-dominated cooling flows. These solutions are used to show how star formation reduces the gas density, thereby lowering the cooling rate, which raises the gas temperature relative to the non-star-forming case. The analytic solutions are also used to estimate the spatial distribution of newly formed stars. It is found that star formation must proceed at a nearly maximal rate if isothermal mass profiles are to result.