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 $\sim49~\rm{arcmin^{2}}$) 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 $V\sim25$, $R\sim25$ and $I\sim24$. Angular correlation analysis is applied to magnitude-limited and color-selected samples of galaxies from the three fields for angular separations ranging from $10-126''$. 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 $r_{0}\sim4~h^{-1}~Mpc$ and $\epsilon\sim0-1$; $r_{0}\sim5-6~h^{-1}~Mpc$ and $\epsilon>1$; or $r_{0}\sim2-3~h^{-1}~ Mpc$ and $\epsilon\sim-1.2$, 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)