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

Abstract

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 (10 10  <  M ⋆  < 10 11 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.