Glimmering in the dark: modeling the low-mass end of the $M_{\bullet }-\sigma$ relation and of the quasar luminosity function

Abstract

The $M_{\bullet }-\sigma$ relation establishes a connection between central black holes (BHs) and their host spheroids. Supported by observations at $M_{\bullet }\gtrsim 10^5{M}_{\odot }$, 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 ($M_{\bullet }\lesssim 10^5{M}_{\odot }$) accreting inefficiently. We predict a departure from the $M_{\bullet }-\sigma$ relation at a transitional BH mass $\sim 10^5{M}_{\odot }$, 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 $\sim 10^5-10^6{M}_{\odot }$. Furthermore, we predict a deficit of BHs shining at bolometric luminosities $\sim 10^{42}\mathrm{erg}{\mathrm{s}}^{-1}$. 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, $<10^{42}\mathrm{erg}{\mathrm{s}}^{-1}$. 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.

Published in ApJ Letters, 2018 September 1. Published version: 6 pages, 3 figures

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