QSO-LRG two-point cross-correlation function and redshift-space distortions

We have measured the bias of QSOs as a function of QSO luminosity at fixed redshift (z < I) 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 Sloan Digital Sky Survey (SDSS) covering a QSO absolute magnitude range, -24.5 < M-bJ < -21.5, and cross-correlate them with 2SLAQ (z approximate to 0.5) and AAOmega (z approximate to 0.7) photometric and spectroscopic LRGs in the same redshift ranges. The spectroscopic QSO samples, in the spectroscopic LRG areas, contain up to 700 QSOs and in photometric LRG areas up to 7000 QSOs. The 2D and 3D cross-clustering measurements are generally in good agreement. Our (2SLAQ) QSO-LRG clustering amplitude (r(0) = 6.98 +/- 0.6 h(-1) Mpc) as measured from the semiprojected cross-correlation function appears similar to the (2SLAQ) LRG-LRG autocorrelation amplitude (r(0) = 7.45 +/- 0.35 h(-1) MPC) and both are higher than the (2QZ + 2SLAQ) QSO-QSO amplitude (r(0) approximate to 5.0 h(-1) Mpc). Our measurements show remarkably little QSO-LRG cross-clustering dependence oil QSO luminosity. This result is unexpected on the basis of simple high-peak biasing models, where more luminous QSOs, are assumed to occupy rarer and so more clustered high-mass peaks. Assuming a standard ACDM model and values for b(LRG) measured from LRG autocorrelation analyses, from the spectroscopic samples at z approximate to 0.55 we find b(Q) = 2.3 +/- 0.5 at M-bJ approximate to -24 and b(Q) = 1.6 +/- 0.3 at M-bJ approximate to -22. Averaging over all the spectroscopic and photometric samples, we find an average value of b(Q) = 1.8 +/- 0.1 at z approximate to 0.6 and M-bJ approximate to -23. The implied dark matter halo mass inhabited by QSOs is approximate to 1013 h(-1) M-circle dot again approximately independent ofQSO luminosity. We have also made a z-space distortion analysis of the QSO-LRG cross-clustering at z approximate to 0.55. The velocity dispersion fitted to QSO-LRG cross-correlation, xi(sigma, pi), at +/- 600 km s(-1) is close to that expected given the larger QSO redshift errors. The dynamical in fall result for the combined 2SLAQ, 2QZ and SDSS QSO sample gives beta(Q) = 0.23 +/- 0.15 which implies b(Q) = 3.2 +/- 2.1, assuming the standard cosmological model. Although noisier, this latter value is consistent with the value of b(Q) = 1.9 +/- 0.2 obtained from the amplitude of the cross-correlation function in the same redshift range.