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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 AGN activity within star-forming and quiescent galaxies, as a function of stellar mass (from $10^{8.5}-10^{11.5} M_\odot$) and redshift (to $z \sim 4$). We adopt near-infrared selected samples of galaxies from the CANDELS and UltraVISTA 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 toward lower $\lambda_{sBHAR}$, a steep cutoff at $\lambda_{sBHAR} \gtrsim 0.1-1$ (in Eddington equivalent units), and a turnover or flattening at $\lambda_{sBHAR} \lesssim 10^{-3}-10^{-2}$. 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 toward 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 ($z\gtrsim2$) quiescent galaxies thus reaches $\sim$20 per cent, comparable to the duty cycle in star-forming galaxies of equivalent stellar mass and redshift., Comment: 20 pages + 3 appendices (27 pages total) with 15 figures. The sketch shown in Figure 9 summarizes our findings. Data tables available at http://doi.org/10.5281/zenodo.1009605 . Updated FAST SED fitting code available at https://github.com/jamesaird/FAST . This is a pre-copyedited, author-produced version of an article accepted for publication in MNRAS following peer review

We use deep Chandra imaging to measure the distribution of X-ray luminosities (L_X) for samples of star-forming galaxies as a function of stellar mass and redshift, using a Bayesian method to push below the nominal X-ray detection limits. Our luminosity distributions all show narrow peaks at L_X < 10^{42} erg/s that we associate with star formation, as opposed to AGN that are traced by a broad tail to higher L_X. Tracking the luminosity of these peaks as a function of stellar mass reveals an "X-ray main sequence" with a constant slope ~0.63 +/- 0.03 over 8.5 < log M*/Msun < 11.5 and 0.1 < z < 4, with a normalization that increases with redshift as (1+z)^{3.79+/-0.12}. We also compare the peak X-ray luminosities with UV-to-IR tracers of star formation rates (SFRs) to calibrate the scaling between L_X and SFR. We find that L_X \propto SFR^{0.83} x (1+z)^{1.3}, where the redshift evolution and non-linearity likely reflect changes in high-mass X-ray binary populations of star-forming galaxies. Using galaxies with a broader range of SFR, we also constrain a stellar-mass-dependent contribution to L_X, likely related to low-mass X-ray binaries. Using this calibration, we convert our X-ray main sequence to SFRs and measure a star-forming main sequence with a constant slope ~0.76+/-0.06 and a normalization that evolves with redshift as (1+z)^{2.95+/-0.33}. Based on the X-ray emission, there is no evidence for a break in the main sequence at high stellar masses, although we cannot rule out a turnover given the uncertainties in the scaling of L_X to SFR., 18 pages + 4 appendices (27 pages total) with 13 figures. The main results are shown by Figures 3 and 4. This is a pre-copyedited, author-produced version of an article accepted for publication in MNRAS following peer review