Measuring the Angular Correlation Function for Faint Galaxies in High Galactic Latitude Fields

A photometric survey of faint galaxies in three high Galactic latitude fields (each $\sim 49\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{m}\mathrm{i}{\mathrm{n}}^2$) with sub-arcsecond seeing is used to study the clustering properties of the faint galaxy population. Multi-color photometry of the galaxies has been obtained to magnitude limits of $V\sim 25$, $R\sim 25$ and $I\sim 24$. Angular correlation analysis is applied to magnitude-limited and color-selected samples of galaxies from the three fields for angular separations ranging from $10-{126}^{\mathrm{\prime }\mathrm{\prime }}$. General agreement is obtained with other recent studies which show that the amplitude of the angular correlation function, $\omega (\theta )$, is smoothly decreasing as a function of limiting magnitude. The observed decline of $\omega (\theta )$ rules out the viability of ``maximal merger’’ galaxy evolution models. Using redshift distributions extrapolated to faint magnitude limits, models of galaxy clustering evolution are calculated and compared to the observed I-band $\omega (\theta )$. Faint galaxies are determined to have correlation lengths and clustering evolution parameters of either $r_0\sim 4h^{-1}Mpc$ and $ϵ\sim 0-1$; $r_0\sim 5-6h^{-1}Mpc$ and $ϵ>1$; or $r_0\sim 2-3h^{-1}Mpc$ and $ϵ\sim -1.2$, assuming $q_0=0.5$ and with $h=H_{0}/100~ km~s^{-1}~Mpc^{-1}$. The latter case is for clustering fixed in co-moving coordinates and is probably unrealistic since most local galaxies are observed to be more strongly clustered. No significant variations in the clustering amplitude as a function of color are detected, for all the color-selected galaxy samples considered. (Abridged)