The quasar-LBG two-point angular cross-correlation function at z ∼ 4 in the cosmos field

In order to investigate the origin of quasars, we estimate the bias factor for low-luminosity quasars at high redshift for the first time. In this study, we use the two-point angular cross-correlation function (CCF) for both low-luminosity quasars at $-24<M_{1450}<-22$ and Lyman-break galaxies (LBGs). Our sample consists of both 25 low-luminosity quasars (16 objects are spectroscopically confirmed low-luminosity quasars) in the redshift range $3.1<z<4.5$ and 835 color-selected LBGs with $z_{LBG}^{\prime }<25.0$ at z ∼ 4 in the COSMOS field. We have performed our analysis for the following two quasar samples: (1) the spectroscopic sample (the 16 quasars confirmed by spectroscopy), and (2) the total sample (the 25 quasars including 9 quasars with photometric redshifts). The bias factor for low-luminosity quasars at z ∼ 4 is derived by utilizing the quasar-LBG CCF and the LBG auto-correlation function. We then obtain the 86% upper limits of the bias factors for low-luminosity quasars, which are 5.63 and 10.50 for the total and the spectroscopic samples, respectively. These bias factors correspond to the typical dark matter halo masses, log $\left(M_{DM}/\right(h^{-1}{M}_{\odot }\left)\right)=$ 12.7 and 13.5, respectively. This result is not inconsistent with the predicted bias for quasars that is estimated by the major merger models.