THE SPATIAL CLUSTERING OFROSATALL-SKY SURVEY AGNs. II. HALO OCCUPATION DISTRIBUTION MODELING OF THE CROSS-CORRELATION FUNCTION

Abstract

This is the second paper of a series that reports on our investigation of the clustering properties of AGNs in the ROSAT All-Sky Survey (RASS) through cross-correlation functions (CCFs) with Sloan Digital Sky Survey (SDSS) galaxies. In this paper, we apply the Halo Occupation Distribution (HOD) model to the CCFs between the RASS Broad-line AGNs with SDSS Luminous Red Galaxies (LRGs) in the redshift range 0.16 < z < 0.36 that was calculated in paper I. In our HOD modeling approach, we use the known HOD of LRGs and constrain the HOD of the AGNs by a model fit to the CCF. For the first time, we are able to go beyond quoting merely a 'typical' AGN host halo mass, M h , and model the full distribution function of AGN host dark matter halos. In addition, we are able to determine the large-scale bias and the mean M h more accurately. We explore the behavior of three simple HOD models. Our first model (Model A) is a truncated power-law HOD model in which all AGNs are satellites. With this model, we find an upper limit to the slope (α) of the AGN HOD that is far below unity. The other two models have a central component, which has a step function form, where the HOD is constant above a minimum mass, without (Model B) or with (Model C) an upper mass cutoff, in addition to the truncated power-law satellite component, similar to the HOD that is found for galaxies. In these two models we find that the upper limits on α are still below unity, with α 0.95 and α 0.84 for Model B and C respectively. Our analysis suggests that the satellite AGN occupation increases slower than, or may even decrease with, M h in contrast to the satellite HODs of luminosity-threshold samples of galaxies, which, in contrast, grow approximately as N s ∝ M α h with α ≈ 1. These results are consistent with observations that the AGN fraction in groups and clusters decreases with richness.

The dark matter haloes of moderate luminosity X-ray AGN as determined from weak gravitational lensing and host stellar masses

“…Reliable constraints on satellite fractions derived from HOD modelling are limited by modelling uncertainties (e.g. Miyaji et al 2011;Shen et al 2013). A perhaps more robust estimate of satellite fractions may be obtained by measuring the effects of satellite peculiar velocities on the 2D redshift space correlation function.…”

“…Instead, our main point here is to demonstrate that, under the assumption that active and inactive galaxies inhabit similar dark matter environments, the SHMR-based approach advocated here makes firm predictions for the shape and normalization of the AGN occupation functions. Miyaji et al (2011) investigated three different HOD parameterizations to model the cross-correlation function between ROSAT All-Sky Survey detected AGN and SDSS LRGs. Among the three models explored by Miyaji et al (2011), their model B provides the best description of the HODs presented here.…”

“…Miyaji et al (2011) investigated three different HOD parameterizations to model the cross-correlation function between ROSAT All-Sky Survey detected AGN and SDSS LRGs. Among the three models explored by Miyaji et al (2011), their model B provides the best description of the HODs presented here. This is a model that is similar to those used for threshold galaxy samples but with an additional free parameter f A that allows the global normalization of N cen to float.…”

“…Li et al 2006;Coil et al 2009;Gilli et al 2009;Allevato et al 2011;Miyaji et al 2011;Krumpe et al 2012;Koutoulidis et al 2013;Mountrichas et al 2013;Shen et al 2013) or the weak gravitational lensing of AGN host galaxies (Mandelbaum et al 2009). Halo masses (hereafter M h ) are typically inferred from these types of approaches by measuring the mean large-scale bias of a given sample.…”

“…While an HOD-type approach may work well for galaxy samples defined by simple luminosity thresholds, it is less clear which parametric form should be adopted for occupation functions when considering AGN-type samples (e.g. Allevato et al 2011;Miyaji et al 2011;Kayo & Oguri 2012;Richardson et al 2013). The AGN duty cycle relative to haloes is unknown, which leads to large uncertainties in both the shape and normalization of the AGN occupation functions.…”