QSOs and galaxies: lensing, clustering and redshift-space distortions

Abstract

The aim of this thesis is to analyze statistically the available QSO, LRG, galaxy and cluster samples in order to estimate the QSO-galaxy lensing anti-correlation signal and measure the mass of foreground galaxies and clusters and to estimate the QSO-LRG clustering amplitude, the QSO bias and their dependence on QSO luminosity. We also investigate the behaviour of the group-galaxy infall parameter and their rms velocity dispersions for different group memberships. The aim here is to make dynamical estimates of the group masses to check the QSO lensing results. We first cross-correlate the SDSS photo-z, g < 21, 1.0 < Z(_p) < 2.2 QSOs with g < 21 galaxies and clusters in the same areas. The anti-correlation found is somewhat less than the results of Myers et al. based on 2QZ QSOs. But contamination of the QSOs by low redshift NELGs and QSOs can cause underestimation of the anticorrelation lensing signal. Correcting for such low redshift contamination at the levels indicated by our spectroscopic checks suggests that the effect is generally small for QSO cross-correlations with g < 21 galaxies but may be an issue for fainter galaxy samples. Thus when this correction is applied to the photo-z QSO sample of Scranton et al. the anti-correlation increases and the agreement with the 2QZ results of Myers et al. is improved. When we also take into account the fainter r < 21 galaxy limit of Scranton et al. as opposed to g < 21 for Myers et al., the two observational results appear to be in very good agreement. We then measure the bias of QSOs as a function of QSO luminosity at fixed redshift (z < 1) by cross-correlating them with Luminous Red Galaxies (LRGs) in the same spatial volume, hence breaking the degeneracy between QSO luminosity and redshift. We use three QSO samples from 2SLAQ, 2QZ and SDSS covering a QSO absolute magnitude range -24.5 < M(_bj) < -21.5, and cross-correlate them with 2SLAQ (z ≈ 0.5) and AAOmega (z ≈ 0.7) photometric and spectroscopic LRGs in the same redshift ranges. The 2-D and 3-D cross-clustering measurements are generally in good agreement. Our (2SLAQ) QSO-LRG clustering amplitude (r(_0) = 6.8 (^+0.1_-0.3)h(^-1)Mpc) as measured from the semi-projected cross-correlation function appears similar to the (2SLAQ) LRG-LRG auto-correlation amplitude (r(_0) = 7.45 ± 0.35h(^-1)Mpc) and both are higher than the (2QZ-t-2SLAQ) QSO-QSO amplitude (r(_0) ≈ 5.0h(^-1)Mpc). Our measurements show remarkably little QSO-LRG cross- clustering dependence on QSO luminosity. Assuming a standard ACDM model and values for b(_LRG) measured from LRG autocorrelation analyses, we find b(_Q) = 1.45 ± 0.11 at M(_bj) ≈ -24 and b(_Q) = 1.90 ± 0.16 at M(_bj) ≈ -22. We also find consistent results for the QSO bias from a z-space distortion analysis of the QSO-LRG cross-clustering at z ≈ 0.55. The velocity dispersions fitted to QSO-LRG cross-correlation, ع (σ,π), at 680 kms(^-1) are intermediate between those for QSO-QSO and LRG-LRG clustering, as expected given the larger QSO redshift errors. The dynamical infall results give ẞ(_Q) = 0.55 ± 0.10, implying b(_Q) = 1.4 ± 0.2. Thus both the z-space distortion and the amplitude analyses yield b(_Q) ≈ 1.5 at M(_bj) ≈ -23. The implied dark matter halo mass inhabited by QSOs at z ≈ 0.55 is ~ 10(^13)h(^-1)M(_ʘ), again approximately independent of QSO luminosity. Prompted by the indications from QSO lensing that there may be more mass associated with galaxy groups than expected from virial analyses, we make new dynamical infall estimates of the masses associated with 2PIGG groups and clusters. We analyse the redshift distortions in the cluster-galaxy cross-correlation function as a function of cluster membership, cross-correlating z < 0.12 2PIGG clusters and groups with the full 2dF galaxy catalogue. We make estimates of the dynamical infall parameter, ẞ, and new estimates of the group velocity dispersions for group membership classes out to z < 0.12. We first find that, out to 30-40h(^-1)Mpc, the amplitude of the full 3-D redshift space cross-correlation function, ع (_cg), rises monotonically with group membership. We use a simple linear-theory infall model to fit ع (σ,π), in the range 5 < s < 40h(^-1) Mpc. We find that the ẞ versus membership relation for the data shows a minimum at intermediate group membership n ≈ 20 or L ≈ 2 x l0(^11)h(^-2)L(_ʘ), implying that the bias and hence M/L ratios rise by a significant factor (≈ 5x) both for small groups and rich clusters. The minimum for the mocks is at a 2 - 3x lower luminosity than for the data. However, the mocks also show a systematic shift between the location of the ẞ minimum and the M/L minimum at L ≈ l0(^11)h(^-2)L(_ʘ), given by direct calculation using the known DM distribution. Our overall conclusion is that bias estimates from dynamical infall appear to support the minimum in star-formation efficiency at intermediate halo masses. Nevertheless, there may still be significant systematic problems arising from measuring ẞ x (^1/_b) ∂P(_mass) /∂P(_gaiaxies) using large-scale infall rather than M/L using small-scale velocity dispersions