The real-space clustering of luminous red galaxies around z<0.6 quasars in the Sloan Digital Sky Survey

TL;DR

This study measures the real-space clustering of luminous red galaxies (LRGs) around low-redshift quasars (0.25<z<0.6) using SDSS DR5 data, employing a novel angular estimator and halo-model interpretation to derive the halo occupation distribution of LRGs and the quasar environment. The quasar–LRG cross-correlation is well described by a power law with slope about 1.8 and a scale length near $r_0\approx 6\,h^{-1}$ Mpc, yielding a large-scale quasar bias of $b_{QSO}\approx 1.09\pm0.15$ at $z\approx 0.43$, consistent with halos of mean mass $\sim10^{12}\,h^{-1}M_\\odot$ and showing little evolution with redshift or luminosity. The small-scale signal, interpreted with mock LRG catalogs, requires a satellite fraction $>25\%$ and favors halo-occupancy models where quasars inhabit halos with a range of masses and satellite configurations, implying quasar hosts with stellar masses $M_{\star}<10^{11}\,h^{-1}M_\odot$ and short lifetimes $t_Q<10^7$ yr. Together, these results constrain quasar triggering and fueling mechanisms and demonstrate the power of cross-correlation analyses with well-characterized photometric galaxy samples. The work highlights the value of forward-modeling with mock catalogs to link observed clustering to the underlying halo occupation and galaxy-halo connection.

Abstract

We measure the clustering of a sample of photometrically selected luminous red galaxies around a low redshift (0.2<z<0.6) sample of quasars selected from the Sloan Digital Sky Survey Data Release 5. We make use of a new statistical estimator to obtain precise measurements of the LRG auto-correlations and constrain halo occupation distributions for them. These are used to generate mock catalogs which aid in interpreting our quasar-LRG cross correlation measurements. The cross correlation is well described by a power law with slope 1.8\pm0.1 and r_0=6\pm0.5 h^{-1} Mpc, consistent with observed galaxy correlation functions. We find no evidence for `excess' clustering on 0.1 Mpc scales and demonstrate that this is consistent with the results of Serber et al (2006) and Strand et al (2007), when one accounts for several subtleties in the interpretation of their measurements. Combining the quasar-LRG cross correlation with the LRG auto-correlations, we determine a large-scale quasar bias b_QSO = 1.09\pm0.15 at a median redshift of 0.43, with no observed redshift or luminosity evolution. This corresponds to a mean halo mass <M>~ 10^{12} h^{-1} M_sun, Eddington ratios from 0.01 to 1 and lifetimes less than 10^{7} yr. Using simple models of halo occupation, these correspond to a number density of quasar hosts greater than 10^{-3} h^{3} Mpc^{-3} and stellar masses less than 10^{11} h^{-1} M_sun. The small-scale clustering signal can be interpreted with the aid of our mock LRG catalogs, and depends on the manner in which quasars inhabit halos. We find that our small scale measurements are inconsistent with quasar positions being randomly subsampled from halo centers above a mass threshold, requiring a satellite fraction > 25 per cent.

Figures (11)

• Figure 1: The redshift distribution of the quasars [top] and LRGs [bottom] used in this analysis. The LRG redshift distributions are derived from the observed photometric redshift distribution, after deconvolving the redshift errors. The dotted lines show the redshift distribution for the six individual $dz_{\rm photo}=0.05$ LRG samples. The vertical lines mark the boundaries of the three quasar redshift slices we consider -- $0.25 < z < 0.35$ (dotted), $0.33 < z < 50$ (short-dashed) and $0.45 < z < 0.6$ (long-dashed).
• Figure 2: The angular distribution of our quasar sample, plotted in an RA-$\cos(\delta)$ equal-area rectilinear projection. The angular mask for the quasars is both determined by the spectroscopic coverage, as well as the overlap with the photometric LRG sample.
• Figure 3: The conditional distribution of absolute magnitude with redshift for our sample of QSOs. The lines plot the 16, 50 and 84 per cent contours. The lower panel plots the absolute magnitude relative to $M_\star$, estimated from the 2dF and 2SLAQ survey. The flattening/upturn at low redshift is due to the $M_i=-22.0$ cut on the sample, to minimize contamination from the host galaxy. The vertical lines (as in Fig. \ref{['fig:dndz']}) show the redshift boundaries of our samples.
• Figure 4: The observed $\omega$ for the six LRG redshift slices, as a function of the filter scale $\theta_s$. Recall that $\omega$ probes the angular correlation function on scales $\sim\theta_s/2$; the corresponding physical scales are also shown. We also plot the best fit models, both from the HaloFit fitting formula [dashed/red] for the nonlinear dark matter clustering, as well as from our halo model fits [solid/blue]. The dotted vertical line marks the angular scale beyond which we fit the HaloFit models. These fits deviate from the observed clustering on small scales; LRGs are not distributed like the dark matter on these scales. The halo model correlation functions are estimated from the same realizations in the $500\,h^{-1}$Mpc simulation that we use to interpret the quasar-LRG cross-correlations. Note that the data are well fit by the halo model on both small and large scales.
• Figure 5: Best fit HODs for the six LRG slices we consider in this paper. The shaded region denotes the errors, as estimated by Monte Carlo.