Probing black hole accretion tracks, scaling relations and radiative
  efficiencies from stacked X-ray active galactic nuclei
  The masses of supermassive black holes at the centres of local galaxies
appear to be tightly correlated with the mass and velocity dispersions of their
galactic hosts. However, the local Mbh-Mstar relation inferred from dynamically
measured inactive black holes is up to an order-of-magnitude higher than some
estimates from active black holes, and recent work suggests that this
discrepancy arises from selection bias on the sample of dynamical black hole
mass measurements. In this work we combine X-ray measurements of the mean black
hole accretion luminosity as a function of stellar mass and redshift with
empirical models of galaxy stellar mass growth, integrating over time to
predict the evolving Mbh-Mstar relation. The implied relation is nearly
independent of redshift, indicating that stellar and black hole masses grow, on
average, at similar rates. Matching the de-biased local Mbh-Mstar relation
requires a mean radiative efficiency ~0.15, in line with theoretical
expectations for accretion onto spinning black holes. However, matching the
"raw" observed relation for inactive black holes requires a mean radiative
efficiency around 0.02, far below theoretical expectations. This result
provides independent evidence for selection bias in dynamically estimated black
hole masses, a conclusion that is robust to uncertainties in bolometric
corrections, obscured active black hole fractions, and kinetic accretion
efficiency. For our fiducial assumptions, they favour moderate-to-rapid spins
of typical supermassive black holes, to achieve a mean radiative efficiency
~0.12-0.20. Our approach has similarities to the classic Soltan analysis, but
by using galaxy-based data instead of integrated quantities we are able to
focus on regimes where observational uncertainties are minimized.
