Abstract The spatial clustering of QSOs is an important measurable quantity which can be used to infer the properties of dark matter halos that host them. We construct a simple QSO model to explain the linear bias of QSOs measured by recent observations and explore the properties of dark matter halos that host a QSO. We assume that major mergers of dark matter halos can lead to the triggering of QSO phenomena, and the evolution of luminosity for a QSO generally shows two accretion phases, i.e., initially having a constant Eddington ratio due to the self-regulation of the accretion process when supply is sufficient, and then declining in rate with time as a power law due to either diminished supply or long term disk evolution. Using a Markov Chain Monte Carlo method, the model parameters are constrained by fitting the observationally determined QSO luminosity functions (LFs) in the hard X-ray and in the optical band simultaneously. Adopting the model parameters that best fit the QSO LFs, the linear bias of QSOs can be predicted and then compared with the observational measurements by accounting for various selection effects in different QSO surveys. We find that the latest measurements of the linear bias of QSOs from both the SDSS and BOSS QSO surveys can be well reproduced. The typical mass of SDSS QSOs at redshift 1.5 < z < 4.5 is ~ (3 − 6) × 1012 h−1M⊙ and the typical mass of BOSS QSOs at z ~ 2.4 is ~ 2 × 1012 h−1M⊙. For relatively faint QSOs, the mass distribution of their host dark matter halos is wider than that of bright QSOs because faint QSOs can be hosted in both big halos and smaller halos, but bright QSOs are only hosted in big halos, which is part of the reason for the predicted weak dependence of the linear biases on the QSO luminosity.

Keywords black hole physics — galaxies: active — cosmology

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