Clustering of Low-Redshift (z <= 2.2) Quasars from the Sloan Digital Sky Survey

TL;DR

This study measures the clustering of low-redshift quasars (0.3 ≤ z ≤ 2.2) using a homogeneous SDSS DR5 quasar sample, the largest of its kind. By estimating the redshift-space and projected two-point correlation functions with a Landy–Szalay approach and constructing matching random catalogs, the authors derive a real-space correlation length of about $r_{0} \approx 5.5$ h⁻¹ Mpc and a slope near $\gamma ≈ 1.9$, with minimal evolution across redshift. They infer a linearly biased tracing of matter, $b(z)$ rising from ~1.4 at z ~ 0.5 to ~3 at z ~ 2.2, implying host dark matter halos of roughly $M_{DMH} \sim 2 \times 10^{12} h^{-1} M_{\odot}$ that do not evolve strongly in mass over this interval. These results closely align with previous surveys and CDM-based models, and while they constrain quasar fueling scenarios, deeper data at fainter luminosities are needed to decisively distinguish competing evolutionary models.

Abstract

We present measurements of the quasar two-point correlation function, ξ_{Q}, over the redshift range z=0.3-2.2 based upon data from the SDSS. Using a homogeneous sample of 30,239 quasars with spectroscopic redshifts from the DR5 Quasar Catalogue, our study represents the largest sample used for this type of investigation to date. With this redshift range and an areal coverage of approx 4,000 deg^2, we sample over 25 h^-3 Gpc^3 (comoving) assuming the current LCDM cosmology. Over this redshift range, we find that the redshift-space correlation function, xi(s), is adequately fit by a single power-law, with s_{0}=5.95+/-0.45 h^-1 Mpc and γ_{s}=1.16+0.11-0.16 when fit over s=1-25 h^-1 Mpc. Using the projected correlation function we calculate the real-space correlation length, r_{0}=5.45+0.35-0.45 h^-1 Mpc and γ=1.90+0.04-0.03, over scales of rp=1-130 h^-1 Mpc. Dividing the sample into redshift slices, we find very little, if any, evidence for the evolution of quasar clustering, with the redshift-space correlation length staying roughly constant at s_{0} ~ 6-7 h^-1 Mpc at z<2.2 (and only increasing at redshifts greater than this). Comparing our clustering measurements to those reported for X-ray selected AGN at z=0.5-1, we find reasonable agreement in some cases but significantly lower correlation lengths in others. We find that the linear bias evolves from b~1.4 at z=0.5 to b~3 at z=2.2, with b(z=1.27)=2.06+/-0.03 for the full sample. We compare our data to analytical models and infer that quasars inhabit dark matter haloes of constant mass M ~2 x 10^12 h^-1 M_Sol from redshifts z~2.5 (the peak of quasar activity) to z~0. [ABRIDGED]

Figures (26)

• Figure 1: The SDSS DR5 Quasar $L-z$ plane for the DR5Q (black points) and the UNIFORM sample (red points). The affect of the $i=19.1$ magnitude limit can clearly be seen. $M_{i}$ is the $i$-band absolute magnitude at the plotted redshift where we use the $K$-correction given by Table 4 of Richards06.
• Figure 2: The SDSS DR5 Quasar $N(z)$. The solid (red) histogram shows the quasar redshift distribution for the PRIMARY sample, while the dashed (blue) histogram shows the redshift distribution for the UNIFORM sample. The thin lines for both PRIMARY and UNIFORM do not include the $0.3 \leq z \leq 2.2$ cuts. As a comparison, the full DR5Q sample is given by the dotted (black) histogram.
• Figure 3: The SDSS Quasar redshift-space 2PCF, $\xi(s)$, from the UNIFORM sample (filled circles). The solid line shows the best fit single power-law model over $1 \leq s \leq 25.0 ~h^{-1}~{\rm Mpc}$, while the dotted line shows the best fit single power-law model over $1 \leq s \leq 100.0 ~h^{-1}~{\rm Mpc}$. The lower panel shows the $\xi(s)$ behaviour near zero on a linear scale. The quoted errorbars are jackknife errors from the diagonal elements of the covariance matrix.
• Figure 4: The Quasar redshift-space 2PCF, $\xi(s)$, from the UNIFORM sample as in Fig. \ref{['fig:xis_DR5_UNI22']}. Also shown are the redshift-space correlation functions from the 2QZ Croom05, shown as cerulean filled squares connected with a dotted line, and the 2SLAQ QSO survey daAngela08, shown as the red filled squares connected by the dashed line. There is excellent agreement between the three surveys.
• Figure 5: The SDSS Quasar redshift-space 2PCF, $\xi(s)$, for our UNIFORM sample over the redshift range $0.3 \leq z \leq2.2$ at very large scales. Jackknife errors are plotted. The data are consistent with $\xi(s)=0$ out to scales of $s\sim3000 ~h^{-1}~{\rm Mpc}$, which is the largest scales well-sampled by SDSS.