Are Hubble Deep Field galaxy counts whole numbers?

The Hubble Deep Field (HDF) offers the best view to date of the optical sky at faint magnitudes and small angular scales. Early reports suggested that faint source counts continue to rise to the completeness limit of the data, which implies a very large number of galaxies. In this Letter, we use the two-point angular correlation function and number-magnitude relation of sources within the HDF in order to assess their nature. We find that the correlation peaks between 0.'' 25 and 0.'' 4 with amplitude of 2 or greater and is much higher for the smallest objects. This angular scale corresponds to physical scales of order 1 kpc for redshifts z greater than or similar to 1. The correlation must therefore derive from objects with subgalactic separations. At faint magnitudes, the counts satisfy the relation number proportional to 1/flux, which is expected for images that are subdivisions of larger ones. Several explanations for these observed correlations are possible, but a conservative explanation can suffice to produce our results. Since high-redshift space (z greater than or similar to 0.5) dominates the volume of the sample, observational redshift effects are important. Rest-frame ultraviolet radiation appears in the HDF's visible and near-UV bands, and surface brightness dimming enhances the relative brightness of unresolved objects versus resolved objects. Both work to increase the prominence of compact star-forming regions over diffuse stellar populations. Thus, a ''normal'' gas-rich galaxy at high redshift can appear clumpy and asymmetric in the visible bands. For sufficiently faint and distant objects, the compact star-forming regions in such galaxies peak above undetectable diffuse stellar backgrounds. Our results do not exclude asymmetric formation or fragmentation scenarios.