The halo occupation distribution of active galactic nuclei

Using a fully cosmological hydrodynamic simulation that self-consistently incorporates the growth and feedback of supermassive black holes and the physics of galaxy formation, we examine the effects of environmental factors (e.g. local gas density and black hole feedback) on the halo occupation distribution of low-luminosity active galactic nuclei (AGN). We decompose the mean occupation function into central and satellite contribution and compute the conditional luminosity functions (CLFs). The CLF of the central AGN follows a lognormal distribution with the mean increasing and scatter decreasing with increasing redshifts. We analyse the light curves of individual AGN and show that the peak luminosity of the AGN has a tighter correlation with halo mass compared to instantaneous luminosity. We also compute the CLF of satellite AGN at a given central AGN luminosity. We do not see any significant correlation between the number of satellites with the luminosity of the central AGN at a fixed halo mass. We also show that for a sample of AGN with luminosity above 10⁴² erg s^-1 the mean occupation function can be modelled as a softened step function for central AGN and a power law for the satellite population. The radial distribution of AGN inside haloes follows a power law at all redshifts with a mean index of -2.33 ± 0.08. Incorporating the environmental dependence of supermassive black hole accretion and feedback, our formalism provides a theoretical tool for interpreting current and future measurements of AGN clustering.