We study the mass of quasar-hosting dark matter halos at z \sim 6 and further constrain the fraction of dark matter halos hosting an active quasar f _ { on } and the quasar beaming angle i _ { max } using observations of CII lines in the literature .
We make assumptions that ( 1 ) more massive halos host brighter quasars , ( 2 ) a fraction of the halos host active quasars with a certain beaming angle , ( 3 ) cold gas in galaxies has rotational velocity V _ { circ } = \alpha V _ { max } , and that ( 4 ) quasars point randomly on the sky .
We find that for a choice of specific \alpha \gtrsim 1 , the most likely solution has f _ { on } < 0.01 , corresponding to a small duty cycle of quasar activity .
However , if we marginalize over \alpha , for some choices of a prior a second solution with f _ { on } = 1 appears .
Overall , our the constraints are highly sensitive to \alpha and hence inconclusive .
Stronger constraints on f _ { on } can be made if we better understand the dynamics of cold gas in these galaxies .