  The connection between active galactic nuclei (AGN) and their host dark
matter halos provides powerful insights into how supermassive black holes
(SMBHs) grow and coevolve with their host galaxies. Here we investigate the
impact of observational AGN selection on the AGN halo occupation distribution
(HOD) by forward-modeling AGN activity into cosmological N-body simulations. By
assuming straightforward relationships between the SMBH mass, galaxy mass, and
(sub)halo mass, as well as a uniform broken power law distribution of Eddington
ratios, we find that luminosity-limited AGN samples result in biased HOD
shapes. While AGN defined by an Eddington ratio threshold produce AGN fractions
that are flat across halo mass (unbiased by definition), luminosity-limited AGN
fractions peak around galaxy-group-sized halo masses and then decrease with
increasing halo mass. With higher luminosities, the rise of the AGN fraction
starts at higher halo masses, the peak is shifted towards higher halo masses,
and the decline at higher halo masses is more rapid. These results are
consistent with recent HOD constraints from AGN clustering measurements, which
find (1) characteristic halo mass scales of $\log M_{Vir}\sim$ 12 - 13
[$h^{-1}M_{\odot}$] and (2) a shallower rise of the number of satellite AGN
with increasing halo mass than for the overall galaxy population. Thus the
observational biases due to AGN selection can naturally explain the constant,
characteristic halo mass scale inferred from large-scale AGN clustering
amplitudes over a range of redshifts, as well as the measured inconsistencies
between AGN and galaxy HODs. We conclude that AGN selection biases can have
significant impacts on the inferred AGN HOD, and can therefore lead to possible
misinterpretations of how AGN populate dark matter halos and the AGN-host
galaxy connection.
