In Fig. 11, we present the evolution of the quasar bolometric luminosity function (LF) from $z \sim 3$ down $z \sim 0$. Even though these functions give the number density of accreting black holes in different luminosity bins, they have been a powerful tool to extract information on how MBHs grow with cosmic time, on the geometry of the accretion discs and other fundamental quantities such as the black hole spins and radiative efficiencies. In this work, we only focus on the very bright objects, i.e. ${\gt}10^{45}\, \rm erg\,s^{-1}$, avoiding the comparison with lower luminosity given the current limitations on observational and theoretical models. In particular, from an observational standpoint, the covered area and depth of current surveys pose serious challenges when extracting statistical properties of the LF at the faint end (Siana et al. 2008; Masters et al. 2012; McGreer et al. 2013; Niida et al. 2016; Akiyama et al. 2018). Even more, dust attenuation effects might play an important role in shaping current measurements. On the other hand, current theoretical works show a large excesses at luminosity ${\lt}10^{45}\, \rm erg\,s^{-1}$. In order to reconcile observations with predictions, these works have played with empirical relations for obscuring accreting black holes or with the efficiency of the seeding process (see e.g Degraf, Di Matteo & Springel 2010; Fanidakis et al. 2012; DeGraf & Sijacki 2020). Even though these works provide interesting results shedding light on the nature of low-luminous quasars, the treatment of seeding or dust obscuration is beyond the scope of this paper. As shown in Fig. 11, the fiducial model is compatible with current observations of the quasar LF, showing a sharp cut-off at larger luminosity (Shen et al. 2020). On the other hand, the models with higher gas accretion display a completely different behaviour. Boosting the gas accretion during DI leads to a larger excess of bright quasars at $z \gt 1.0$. For instance, at $z \sim 2$ and for luminosities ${\gt}10^{46}\, \rm erg\,s^{-1}$, the models with $A_{\rm yr^{-1}} \sim 1.92 \times 10^{-15}$ and $A_{\rm yr^{-1}} \sim 2.67 \times 10^{-15}$ are systematically overpredicting the number density by a factor of ${\sim }1$ and ${\sim }2\, \rm dex$, respectively. A similar behaviour is seen at $z \sim 3$. At lower redshifts ($z \lt 1.0$), the model follows both the fiducial results and the observed trends. This is principally caused by the decrease of important DIs events at these redshifts. Regarding the IM models, we can see similar trends at $z \gt 2$, where the bright end of the LF is systematically larger than the observed one. We highlight that the difference is larger with $A_{\rm yr^{-1}} \sim 2.67 \times 10^{-15}$. Interestingly, the excess with respect to the observations is smaller than with the IDI model. This is principally caused by the fact that DI events are more important than mergers at these redshifts (Izquierdo-Villalba et al. 2020). At lower redshifts, we can see larger differences with respect to the fiducial and the IDI models: IM model is systematically overprotecting the bright end of the LF (${\gt}10^{46}\, \rm erg\,s^{-1}$). Such differences can be a factor of 3 (1.5) by $z \sim 0$ up to a factor of 5 (2) at $z \sim 0.5$ for $A_{\rm yr^{-1}} \sim 1.92 \times 10^{-15}$ ($A_{\rm yr^{-1}} \sim 2.67 \times 10^{-15}$).
Citation: Siana et al. 2008
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