  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, 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 (CLF). The CLF of the central AGN follows
a log-normal distribution with the mean increasing and scatter decreasing with
increasing redshifts. We analyze 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
10^42 ergs/s the mean occupation function can be modeled as a softened step
function for central AGN and a power law for the satellite population. The
radial distribution of AGN inside halos 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.
