The Evolving AGN Duty Cycle in Galaxies Since z ∼ 3 as Encoded in the X-Ray Luminosity Function

We present a new modeling of the X-ray luminosity function (XLF) of active galactic nuclei (AGNs) out to z ∼ 3, dissecting the contributions of main-sequence (MS) and starburst (SB) galaxies. For each galaxy population, we convolved the observed galaxy stellar mass (M ⋆) function with a grid of M ⋆-independent Eddington ratio (λ EDD) distributions, normalized via empirical black hole accretion rate (BHAR) to star formation rate (SFR) relations. Our simple approach yields an excellent agreement with the observed XLF since z ∼ 3. We find that the redshift evolution of the observed XLF can only be reproduced through an intrinsic flattening of the λ EDD distribution and with a positive shift of the break λ*, consistent with an antihierarchical behavior. The AGN accretion history is predominantly made by massive (1010 < M ⋆ < 1011 M ⊙) MS galaxies, while SB-driven BH accretion, possibly associated with galaxy mergers, becomes dominant only in bright quasars, at log(L X/erg s−1) > 44.36 + 1.28 × (1 + z). We infer that the probability of finding highly accreting (λ EDD > 10%) AGNs significantly increases with redshift, from 0.4% (3.0%) at z = 0.5%–6.5% (15.3%) at z = 3 for MS (SB) galaxies, implying a longer AGN duty cycle in the early universe. Our results strongly favor a M ⋆-dependent ratio between BHAR and SFR, as BHAR/SFR ∝ , supporting a nonlinear BH buildup relative to the host. Finally, this framework opens potential questions on super-Eddington BH accretion and different λ EDD prescriptions for understanding the cosmic BH mass assembly.