Cloning Hubble Deep Fields: A Model-Independent Measurement of Galaxy Evolution

We present a model-independent method of quantifying galaxy evolution in high- resolution images, which we apply to the Hubble Deep Field (HDF). Our procedure is to k-correct the pixels belonging to the images of a complete set of bright galaxies and then to replicate each galaxy image to higher redshift by the product of its space density, 1/V_{max}, and the cosmological volume. The set of bright galaxies is itself selected from the HDF because presently the HDF provides the highest quality UV images of a redshift-complete sample of galaxies (31 galaxies with I<21.9, \bar{z}=0.5, and for which V/V_{max} is spread fairly). These galaxies are bright enough to permit accurate pixel-by-pixel k-corrections into the restframe UV (\sim 2000 A). We match the shot noise, spatial sampling and PSF smoothing of the HDF, resulting in entirely empirical and parameter free ``no-evolution'' deep fields of galaxies for direct comparison with the HDF. We obtain the following results. Faint HDF galaxies (I>24) are much smaller, more numerous, and less regular than our ``no-evolution'' extrapolation, for any relevant geometry. A higher proportion of HDF galaxies ``dropout'' in both U and B, indicating that some galaxies were brighter at higher redshifts than our ``cloned'' z\sim0.5 population. By simple image transformations we demonstrate that bolometric luminosity evolution generates galaxies which are too large and the contribution of any evolving dwarf population is uninterestingly small. A plausible fit is provided by `mass-conserving' density-evolution, consistent with hierarchical growth of small-scale structure. Finally, we show the potential for improvement using the Advanced Camera, with its superior UV and optical performance.