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We present a study of 107 galaxies, groups, and clusters spanning ~3 ordersof magnitude in mass, ~5 orders of magnitude in central galaxy star formationrate (SFR), ~4 orders of magnitude in the classical cooling rate (dM/dt) of theintracluster medium (ICM), and ~5 orders of magnitude in the central black holeaccretion rate. For each system in this sample, we measure dM/dt using archivalChandra X-ray data and acquire the SFR and systematic uncertainty in the SFR bycombining over 330 estimates from dozens of literature sources. With thesedata, we estimate the efficiency with which the ICM cools and forms stars,finding e_cool = SFR/(dM/dt) = 1.4 +/- 0.4% for systems with dM/dt > 30Msun/yr. For these systems, we measure a slope in the SFR-dM/dt relationgreater than unity, suggesting that the systems with the strongest cool coresare also cooling more efficiently. We propose that this may be related to, onaverage, higher black hole accretion rates in the strongest cool cores, whichcould influence the total amount (saturating near the Eddington rate) anddominant mode (mechanical vs radiative) of feedback. For systems with dM/dt <30 Msun/yr, we find that the SFR and dM/dt are uncorrelated, and show that thisis consistent with star formation being fueled at a low (but dominant) level byrecycled ISM gas in these systems. We find an intrinsic log-normal scatter inSFR at fixed dM/dt of 0.52 +/- 0.06 dex, suggesting that cooling is tightlyself-regulated over very long timescales, but can vary dramatically on shorttimescales. There is weak evidence that this scatter may be related to thefeedback mechanism, with the scatter being minimized (~0.4 dex) in systems forwhich the mechanical feedback power is within a factor of two of the coolingluminosity.

Revisiting the Cooling Flow Problem in Galaxies, Groups, and Clusters of Galaxies