QSO clustering -- III. Clustering in the Large Bright Quasar Survey and evolution of the QSO correlation function

We present results of a clustering analysis for the Large Bright Quasar Survey (LBQS), and combine these with results obtained from other QSO surveys including the Durham/AAT UVX sample (Paper I). We find a weak signal in the LBQS at small scales, ξ(10 h−l Mpc) = 1.86 ± 1.28 (for q0 = 0.5). Combined with other samples we find ξ (10) = 0.83 ±0.29, which is consistent with present-day galaxy clustering, and ξ ≃ (r/6) −1.8. To interpret the evolution of QSO clustering we develop a simple biased model of clustering. Using this model and only the high-redshift samples our biasing model gives an upper limit on present-day QSO clustering of r0(z = 0) = 9.23 ± 1.11 h−1 Mpc (assuming a −1.8 power law), a value which is significantly lower than some previous estimates (Mo & Fang). When we include the observed small amplitude of clustering of z ∼ 0 active galactic nuclei (AGN) (Paper II) in the model fits, we find that the low level of QSO evolution is inconsistent with Ω0 = l, unbiased galaxy, clustering at almost the 3σ level. The low level of QSO clustering evolution is more consistent with low Ω0 or high values of biasing (bqρ≃bgρ>2). At intermediate scales (8–50 h−1 Mpc) we have tested the QSO correlation function (at the average redshift of 1.27) against linear cold dark matter (CDM) predictions normalized to the cosmic microwave background (CMB) results of COBE. For standard CDM (Ω0 = l, Г = 0.5) we find the best-fitting QSO bias to be bqρ(z = 0) = l.40+0.28−0.43 Thus there appears to be a narrow range around bqρ∼2, consistent with both the biased evolution and comparisons to COBE-normalized power spectra, which allows the Ω0 = 1, CDM model to survive. An interesting test of the Ω0 = 1 model should therefore be possible in a larger data set. We also test ACDM, finding a similar bias, bqρ(z = 0) = 1.20 +0.13−0.18. At large scales we find little evidence in the LBQS for the anticorrelation beween 40 and 100 h−1 Mpc seen in the Durham/AAT survey. In the combined sample we find no significant signal on any scale larger than 50 h−l Mpc. Since from simulations we estimate that above 100 h−1 Mpc our errors are at the ± 0.025 level, these QSO clustering observations represent the most accurate upper limit on the amplitude of large-scale structure from redshift survey data.