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

We present a study of 107 galaxies, groups, and clusters spanning ∼3 orders of magnitude in mass, ∼5 orders of magnitude in central galaxy star formation rate (SFR), ∼4 orders of magnitude in the classical cooling rate \dot M_cool \equiv M_gas(r< r_cool)/t_cool of the intracluster medium (ICM), and ∼5 orders of magnitude in the central black hole accretion rate. For each system in this sample, we measure the ICM cooling rate, \dot M_cool, using archival Chandra X-ray data and acquire the SFR and systematic uncertainty in the SFR by combining over 330 estimates from dozens of literature sources. With these data, we estimate the efficiency with which the ICM cools and forms stars, finding ∊_cool \equiv SFR/\dot M_cool = 1.4% +/- 0.4% for systems with \dot M_cool >30 M_☉/yr. For these systems, we measure a slope in the SFR - \dot M_cool relation greater than unity, suggesting that the systems with the strongest cool cores are also cooling more efficiently. We propose that this may be related to, on average, higher black hole accretion rates in the strongest cool cores, which could influence the total amount (saturating near the Eddington rate) and dominant mode (mechanical versus radiative) of feedback. For systems with \dot M_cool < 30 M_☉/yr, we find that the SFR and \dot M_cool are uncorrelated and show that this is consistent with star formation being fueled at a low (but dominant) level by recycled ISM gas in these systems. We find an intrinsic log-normal scatter in SFR at a fixed \dot M_cool of 0.52 ± 0.06 dex (1σ rms), suggesting that cooling is tightly self-regulated over very long timescales but can vary dramatically on short timescales. There is weak evidence that this scatter may be related to the feedback mechanism, with the scatter being minimized (∼0.4 dex) for systems for which the mechanical feedback power is within a factor of two of the cooling luminosity.