Clustering of galaxies at faint magnitudes
Significant uncertainties exist in the measured amplitude of the angular two-point correlation function of galaxies at magnitudes $I\approx26$ and fainter. Published results from HST and ground-based galaxy catalogs seem to differ by as much as a factor of 3, and it is not clear whether the correlation amplitude as a function of magnitude increases or decreases in the faintest magnitude bins. In order to clarify the situation, we present new results from both ground-based and HST galaxy catalogs. The angular two-point correlation function as a function of limiting R and I magnitudes was computed from a galaxy catalog created from the Hubble Deep Field - South (HDF-S) WFPC2 image. The measured amplitudes of the correlation at an angular separation of 1 arcsec are consistent with those measured in the Northern counter part of the field. The flanking fields (FF fields) of the Hubble deep fields were used to extend the magnitude range for which we compute correlation amplitudes towards brighter magnitude bins. This allows easier comparison of the amplitudes to ground based data. The newly measured correlation amplitudes as a function of magnitude limit were compared to previously published measurements at larger separations. For this comparison, the correlation function was approximated by a power law with an index of 0.8. The scatter in the correlation amplitudes is too large to be explained by random errors. We argue that the most likely cause is the assumption that the shape of the correlation function does not depend on the magnitude limit.