Constraints on the Duty Cycles of Quasars at z ∼ 6

Abstract

Abstract We study the mass of quasar-hosting dark matter halos at z ∼ 6 and further constrain the fraction of dark matter halos hosting active quasars f on and the quasar opening angle i max using observations of C ii lines in the literature. We make assumptions that (1) on average more massive halos host quasars with higher peak brightness, (2) cold gas in galaxies has rotational velocity V circ = αV max, where V max is the maximum circular velocity of dark matter particles obtained from DM-only simulation and α ∼ 1 is a free parameter, (3) a fraction f on of the halos host active quasars with a certain opening angle i max, and that (4) quasars point randomly on the sky. We find that for a choice of specific α ≳ 1, the most likely solution has f on < 0.01, corresponding to a small duty cycle of quasar activity. We also apply a bounded flat prior on α and marginalize over it, and we find the most likely f on shift to 1 as the upper-boundary of α decreases below 1. Overall, our constraints are highly sensitive to α and hence inconclusive. Stronger constraints on f on can be made if we better understand the dynamics of cold gas in these galaxies.