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

We present a model-independent method of quantifying galaxy evolution in hi gh-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 co mplete set of bright galaxies and then to replicate each galaxy image to hi gher redshift by the product of its space density, 1/V-max, and the cosmolo gical volume. The set of bright galaxies is itself selected from the HDF, b ecause presently the HDF provides the highest quality UV images of a redshi ft-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 t o permit accurate pixel-by-pixel k-corrections into the rest frame UV (simi lar 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 compa rison with the HDF. In addition, the overcounting rate and the level of inc ompleteness can be accurately quantified by this procedure. We obtain the f ollowing results. Faint HDF galaxies (I > 24) are much smaller, more numero us, and less regular than our no-evolution extrapolation, for any interesti ng geometry. A higher proportion of HDF galaxies "dropout" in both U and B, indicating that some galaxies are brighter at higher redshifts than our "c loned" z similar to 0.5 population.