APM GALAXY SURVEY .3. AN ANALYSIS OF SYSTEMATIC-ERRORS IN THE ANGULAR-CORRELATION FUNCTION AND COSMOLOGICAL IMPLICATIONS

We present measurements of the angular two-point galaxy correlation fu nction, w(theta), from the APM Galaxy Survey. Various estimators of w are investigated using simulated galaxy catalogues and analytic argume nts, and we use the estimators that are least affected by errors in th e galaxy counts. An error analysis of the plate matching procedure in the APM Galaxy Survey shows that residual plate-to-plate errors bias o ur estimates of w by no more than similar to 1 x 10(-3). A direct comp arison between our photometry and external CCD photometry of over 13 0 00 galaxies from the Las Campanas Deep Redshift Survey shows that the rms error in the APM plate zero-points lies in the range 0.04-0.05 mag , in agreement with our previous estimates. This comparison also sets tight limits on the variation of our photometry with right ascension. We find no evidence for systematic errors in the survey correlated wit h the date of plate scan or exposure. We find that atmospheric extinct ion and obscuration by dust in our Galaxy have negligible effect on w. The estimated plate-to-plate errors are independent of limiting magni tude for b(J) < 20. At fainter limits the star-galaxy classification b ecomes less reliable and plate-to-plate variations in the completeness of the survey are introduced. We use deep redshift surveys to estimat e the redshift distribution of galaxies in the APM Galaxy Survey at va rious magnitude limits. These redshift distributions are used to predi ct how w should scale as a function of limiting magnitude. Our estimat es of w are in excellent agreement with the expected scaling relation, providing further evidence that systematic errors in the APM survey a re small. We explicitly remove large-scale structure by filtering the APM galaxy maps and conclude that there is still strong evidence for m ore large-scale structure than predicted by the standard scale-invaria nt cold dark matter (CDM) model. We compare the APM w, and the three-d imensional power spectrum derived by inverting w, with the predictions of scale-invariant CDM models. We show that the observations require Gamma=Omega(0)h in the range 0.2-0.3 and are incompatible with the val ue Gamma=0.5 of the standard CDM model.