Clustering of Low-Redshift (z <= 2.2) Quasars from the Sloan Digital Sky Survey (0903.3230v1)

Abstract: We present measurements of the quasar two-point correlation function, \xi_{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 \gamma_{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 \gamma=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]

• The paper demonstrates that quasar clustering follows a single power-law with a redshift-space correlation length of 5.95 ± 0.45 h⁻¹ Mpc over separations of 1–25 h⁻¹ Mpc.
• It uses an extensive SDSS DR5 sample of 30,239 quasars to confirm minimal clustering evolution consistent with earlier surveys and bias factors rising from 1.4 at z = 0.5 to 3 at z = 2.2.
• Robust methodological corrections reveal that quasars predominantly reside in dark matter haloes of approximately 2×10¹² h⁻¹ M☉, offering key insights into quasar formation and duty cycles.

Overview of Quasar Clustering at Low Redshifts from SDSS

The paper authored by Ross et al. presents an in-depth analysis of the quasar two-point correlation function, specifically targeting objects with redshifts $0.3 \leq z \leq 2.2$. Using data obtained from the Sloan Digital Sky Survey (SDSS) Data Release 5, the paper incorporates a significant sample comprising 30,239 quasars, making it one of the largest quasar clustering analyses to date.

Key results demonstrate that the redshift-space correlation function, $\xi(s)$, conforms well to a single power-law model, specifically characterized by a correlation length $s_0 = 5.95 \pm 0.45 \hmpc$ and a power-law index $\gamma_s = 1.16^{+0.11}_{-0.16}$ when evaluated over separations of $1.0 \leq s \leq 25.0 \hmpc$. This empirical model holds across the examined scales, though deviations are evidenced when extending the fit to $s > 25 \hmpc$, highlighting redshift-space distortions, notably the expected ‘Fingers-of-God’ effect, typically causing elongation along the line of sight due to peculiar velocities of quasars.

In projecting the correlation function, $\wp$, the real-space correlation length was determined to be $r_0 = 5.45^{+0.35}_{-0.45} \hmpc$ with $\gamma=1.90^{+0.04}_{-0.03}$. Notably, clustering results are consistent with those provided by previous surveys such as 2QZ and 2SLAQ, affirming minimal evolution of quasar clustering over the sampled redshift range. This robustness supports the assertion that quasar clustering is largely invariant across the studied epoch, with more significant adjustments only apparent at $z > 1.7$, as suggested by a slight real-space evolution.

Further, by contrasting the SDSS results with clustering data from X-ray selected AGNs, disparities in correlation lengths emerge, underscoring the complexity of quasar host environments. The inferred linear bias factors were observed to evolve from $b \sim 1.4$ at $z=0.5$ to $b \sim 3$ at $z=2.2$, with the overall sample yielding a bias of $b(z=1.27) = 2.06 \pm 0.03$. Combining bias data with models from Sheth and Tormen suggests quasars predominantly inhabit dark matter haloes of mass $M_{\rm halo} \sim 2\times10^{12} h^{-1}\msun$, remaining stable across the studied redshift range.

The paper underscores critical implications for theoretical quasar formation and evolution models. The stability of cluster scales supports scenarios of quasars residing within relatively stable halo masses over cosmic time. This finding may influence perspectives on the evolution of quasar duty cycles, underlying dark matter distributions, and SMBH growth mechanisms. Future analysis could benefit from deeper surveys extending beyond current magnitude limits, providing potentially more discriminative tests of quasar growth models, particularly in reconciling contrasting frameworks such as 'inefficient' versus 'efficient' feedback mechanisms in quasar activity.

Of practical significance, the methodological rigor highlighted in handling systematic biases such as fibre collisions, photometric errors, and sky coverage, sets a standard for large-scale cosmological analyses. The results presented by Ross et al. represent a pivotal step in precision cosmology, offering a robust dataset for future synthesis with cosmological simulations and deep X-ray survey data to further unravel the quasar halo connection and LSS evolution.