Determining Star Formation Rates in X-Ray Cluster Cooling Flows

Many X-ray clusters of galaxies are observed to have cooling flows at their centers. Each of these cooling flows is depositing mass onto a central dominant galaxy at a rate of 10-400 solar masses/yr. With such large accretion rates it seems possible that these accreting galaxies are still being formed through ongoing star formation in their associated cooling flows. In this paper techniques are developed to determine directly the distributions of local star formation rate, mass, gas density, temperature, and velocity from cooling flow X-ray surface brightness data. These techniques take account of the potentially important X-ray emission from star-forming cooling condensations dropping out of the background flow. Surface brightness data with either good or poor energy resolution are considered separately.