We examine the clustering of quasars over a wide luminosity range , by utilizing 901 quasars at \overline { z } _ { phot } \sim 3.8 with -24.73 < M _ { 1450 } < -22.23 photometrically selected from the Hyper Suprime-Cam Subaru Strategic Program ( HSC-SSP ) S16A Wide2 date release and 342 more luminous quasars at 3.4 < z _ { spec } < 4.6 having -28.0 < M _ { 1450 } < -23.95 from the Sloan Digital Sky Survey ( SDSS ) that fall in the HSC survey fields .
We measure the bias factors of two quasar samples by evaluating the cross-correlation functions ( CCFs ) between the quasar samples and 25790 bright z \sim 4 Lyman Break Galaxies ( LBGs ) in M _ { 1450 } < -21.25 photometrically selected from the HSC dataset .
Over an angular scale of \timeform 10.0 ’ ’ to \timeform 1000.0 ’ ’ , the bias factors are 5.93 ^ { +1.34 } _ { -1.43 } and 2.73 ^ { +2.44 } _ { -2.55 } for the low and high luminosity quasars , respectively , indicating no luminosity dependence of quasar clustering at z \sim 4 .
It is noted that the bias factor of the luminous quasars estimated by the CCF is smaller than that estimated by the auto-correlation function ( ACF ) over a similar redshift range , especially on scales below \timeform 40.0 ’ ’ .
Moreover , the bias factor of the less-luminous quasars implies the minimal mass of their host dark matter halos ( DMHs ) is 0.3 - 2 \times 10 ^ { 12 } h ^ { -1 } M _ { \odot } , corresponding to a quasar duty cycle of 0.001 - 0.06 .