Do Current X-Ray Observations Capture Most of the Black-hole Accretion at High Redshifts?

The cosmic black hole accretion density (BHAD) is critical for our understanding of the formation and evolution of supermassive black holes (BHs). However, at high redshifts ($z>3$), X-ray observations report BHADs significantly ($\sim 10$ times) lower than those predicted by cosmological simulations. It is therefore paramount to constrain the high-$z$ BHAD using independent methods other than direct X-ray detections. The recently established relation between star formation rate and BH accretion rate among bulge-dominated galaxies provides such a chance, as it enables an estimate of the BHAD from the star-formation histories (SFHs) of lower-redshift objects. Using the CANDELS Lyman-$\alpha$ Emission At Reionization (CLEAR) survey, we model the SFHs for a sample of 108 bulge-dominated galaxies at $z=$0.7-1.5, and further estimate the BHAD contributed by their high-$z$ progenitors. The predicted BHAD at $z\approx 4$-5 is consistent with the simulation-predicted values, but higher than the X-ray measurements (by $\approx$3-10 times at $z=$4-5). Our result suggests that the current X-ray surveys could be missing many heavily obscured Compton-thick active galactic nuclei (AGNs) at high redshifts. However, this BHAD estimation assumes that the high-$z$ progenitors of our $z=$0.7-1.5 sample remain bulge-dominated where star formation is correlated with BH cold-gas accretion. Alternatively, our prediction could signify a stark decline in the fraction of bulges in high-$z$ galaxies (with an associated drop in BH accretion). JWST and Origins will resolve the discrepancy between our predicted BHAD and the X-ray results by constraining Compton-thick AGN and bulge evolution at high redshifts.