X-rays across the galaxy population - II. The distribution of AGN accretion rates as a function of stellar mass and redshift

We use deep Chandra X-ray imaging to measure the distribution of specific black hole accretion rates (L-X relative to the stellar mass of the galaxy) and thus trace active galactic nucleus (AGN) activity within star-forming and quiescent galaxies, as a function of stellar mass (from 10(8.5) to 10(11.5) M-circle dot) and redshift (to z similar to 4). We adopt near-infrared-selected samples of galaxies from the CANDELS and Ultra VISTA surveys, extract X-ray data for every galaxy, and use a flexible Bayesian method to combine these data and to measure the probability distribution function of specific black hole accretion rates, lambda(sBHAR). We identify a broad distribution of lambda(sBHAR) in both star-forming and quiescent galaxies - likely reflecting the stochastic nature of AGN fuelling with a roughly power-law shape that rises towards lower lambda(sBHAR), a steep cut-off at lambda(sBHAR) greater than or similar to 0.1-1 (in Eddington equivalent units), and a turnover or flattening at lambda(sBHAR) less than or similar to 10(-3) to 10(-2). We find that the probability of a star-forming galaxy hosting a moderate lambda(sBHAR) AGN depends on stellar mass and evolves with redshift, shifting towards higher lambda(sBHAR) at higher redshifts. This evolution is truncated at a point corresponding to the Eddington limit, indicating black holes may self-regulate their growth at high redshifts when copious gas is available. The probability of a quiescent galaxy hosting an AGN is generally lower than that of a star-forming galaxy, shows signs of suppression at the highest stellar masses and evolves strongly with redshift. The AGN duty cycle in high-redshift (z >= 2) quiescent galaxies thus reaches similar to 20 per cent, comparable to the duty cycle in star-forming galaxies of equivalent stellar mass and redshift.