Stochastic Processes as the Origin of the Double Power-law Shape of the Quasar Luminosity Function

The quasar luminosity function (QLF) offers insight into the early coevolution of black holes and galaxies. It has been characterized observationally up to redshift z ∼ 6 with clear evidence of a double power-law shape, in contrast to the Schechter-like form of the underlying dark-matter halo mass function. We investigate a physical origin for the difference in these distributions by considering the impact of stochasticity induced by the processes that determine the quasar luminosity for a given host halo and redshift. We employ a conditional luminosity function and construct the relation between median quasar magnitude versus halo mass ${M}_{\mathrm{UV},{\rm{c}}}({M}_{{\rm{h}}})$ with log-normal in luminosity scatter Σ, and duty-cycle ɛ_DC, and focus on high redshift z ≳ 4. We show that, in order to reproduce the observed QLF, the Σ = 0 abundance matching requires all of the brightest quasars to be hosted in the rarest most massive dark-matter halos (with an increasing ${M}_{\mathrm{UV},{\rm{c}}}/{M}_{{\rm{h}}}$ in halo mass). Conversely, for Σ > 0 the brightest quasars can be overluminous outliers hosted in relatively common dark-matter halos. In this case, the median quasar magnitude versus halo mass relation, M_UV,c, flattens at the high-end, as expected in self-regulated growth due to feedback. We sample the parameter space of Σ and ɛ_DC and show that M_UV,c flattens above ${M}_{{\rm{h}}}\sim {10}^{12}{M}_{\odot }$ for ${\epsilon }_{\mathrm{DC}}\lt {10}^{-2}$ . Models with ɛ_DC ∼ 1 instead require a high mass threshold close to ${M}_{{\rm{h}}}\gtrsim {10}^{13}{M}_{\odot }$ . We investigate the impact of ɛ_DC and Σ on measurements of clustering and find there is no luminosity dependence on clustering for Σ > 0.3, consistent with recent observations from Subaru HSC.