The impact of AGN X-ray selection on the AGN halo occupation distribution

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.