Radio-quiet QSO environments - I. The correlation of QSOs and bj<23 galaxies

In this paper we present results of an analysis of radio-quiet QSO environments. The aim is to determine the relation between QSOs and galaxies as a function of redshift. We cross-correlate a sample of ~150 QSOs from optically and X-ray selected catalogues with faint, bj<23, galaxies. These data allow us to probe the galaxy clustering environment of QSOs out to z~1.0-1.5. Far from giving a positive correlation, at z<1.5 the QSO-galaxy cross-correlation function is marginally negative, with w(theta<120'')=-0.027+-0.020. Colour information suggests that the anti-correlation is most significant between the QSOs and the red galaxy population. We have constructed models to predict the QSO-galaxy cross-correlation, using the known form of the galaxy N(z) at bj<23, and assuming a variety of clustering evolution rates. Cases in which QSOs exist in rich cluster environments are comfortably ruled out at more than 5sigma and the results are more consistent with a `normal' galaxy environment for radio-quiet QSOs. If the small anti-correlation is interpreted as an effect of gravitational lensing, this conclusion is not altered. In this case, the data are only ~1sigma below the low clustering amplitude models, while the high amplitude models are still comfortably rejected. We therefore conclude that these QSOs may not be much more highly biased than optically selected galaxies.