ARE HUBBLE DEEP FIELD GALAXY COUNTS WHOLE NUMBERS

The Hubble Deep Field (HDF) offers the best view to date of the optica l sky at faint magnitudes and small angular scales. Early reports sugg ested that faint source counts continue to rise to the completeness li mit of the data, which implies a very large number of galaxies. In thi s 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 ob jects. This angular scale corresponds to physical scales of order 1 kp c for redshifts z greater than or similar to 1. The correlation must t herefore derive from objects with subgalactic separations. At faint ma gnitudes, the counts satisfy the relation number proportional to 1/flu x, 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 v olume of the sample, observational redshift effects are important. Res t-frame ultraviolet radiation appears in the HDF's visible and near-UV bands, and surface brightness dimming enhances the relative brightnes s of unresolved objects versus resolved objects. Both work to increase the prominence of compact star-forming regions over diffuse stellar p opulations. Thus, a ''normal'' gas-rich galaxy at high redshift can ap pear clumpy and asymmetric in the visible bands. For sufficiently fain t and distant objects, the compact star-forming regions in such galaxi es peak above undetectable diffuse stellar backgrounds. Our results do not exclude asymmetric formation or fragmentation scenarios.