Cloning Hubble Deep Fields. I. A model-independent measurement of galaxy evolution

We present a model-independent method of quantifying galaxy evolution in high-resolution images, a method which we apply to the Hubble Deep Field (HDF). Our procedure is to k-correct all 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, (z) over bar = 0.5, for which V/V-max is spread fairly). These galaxies are bright enough to permit accurate pixel-by-pixel k-corrections into the rest frame UV (similar to 2000 Angstrom). We match the shot noise, spatial sampling, and point-spread function smoothing of the HDF data, resulting in entirely empirical and parameter-free "no-evolution" deep fields of galaxies for direct comparison with the HDF. In addition, the overcounting rate and the level of incompleteness can be accurately quantified by this procedure. 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 interesting geometry. A higher proportion of HDF galaxies "dropout" in both U and B, indicating that some galaxies are brighter at higher redshifts than our "cloned" z similar to 0.5 population.