Glimmering in the Dark: Modeling the Low-mass End of the M •-σ Relation and of the Quasar Luminosity Function

The {M}_\bullet {--}σ relation establishes a connection between central black holes (BHs) and their host spheroids. Supported by observations at {M}_\bullet ≳ {10}⁵ {M}_⊙ , there is limited data on its validity at lower masses. Employing a semi-analytical model to simulate the combined evolution of BHs and their host galaxies, we predict the observational consequences of assuming a bimodality in the accretion efficiency of BHs, with low-mass BHs ({M}_\bullet ≲ {10}⁵ {M}_⊙ ) accreting inefficiently. We predict a departure from the {M}_\bullet {--}σ relation at a transitional BH mass ∼ {10}⁵ {M}_⊙ , with lower-mass BHs unable to reach the mass dictated by the relation and becoming disconnected from the evolution of the host galaxy. This prediction is an alternative to previous works suggesting a flattening of the relation at ∼ {10}⁵{--}{10}⁶ {M}_⊙ . Furthermore, we predict a deficit of BHs shining at bolometric luminosities ∼ {10}⁴² {erg} {{{s}}}^-1. Joined with a detection bias, this could partly explain the scarce number of intermediate-mass BHs detected. Conversely, we predict an increase in source density at lower bolometric luminosities, < {10}⁴² {erg} {{{s}}}^-1. Because our predictions assume a bimodal population of high-redshift BH seeds, future observations of fainter BHs will be fundamental for constraining the nature of these seeds.