The Angular Correlation Function of Galaxies in CDM and CHDM Models

We estimate the angular correlation function for the standard CDM, tilted $n=0.7$ CDM and hybrid (CHDM) models, and compare with observations. When compared with the APM observational results scaled to the Lick depth, there appears to be fair agreement with the estimate from the CHDM model. But a more detailed comparison using the unscaled APM data for the five magnitude slices with $\Delta b_j=0.5$ shows that, in fact, none of the models can actually fit w(theta) for all the slices simultaneously. As $n=0.7$ tilted CDM and SCDM bracket all possible tilted models, we conclude that none of the tilted models is consistent with the APM results. With CHDM, a \wtheta amplitude that is 30\%--40\% too high on scales $\theta < 0.\deg 5$ is predicted for the deepest slices ($b_j\approx 20$). We find that no reasonable simple variation of the parameters for the luminosity function or for the evolution of the correlation function with redshift could change the situation. Thus, the discrepancy between the APM data and the CHDM model, though small, seems to be real.