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/Vmax, 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, z̄ = 0.5, and for which V/Vmax is spread fairly). These galaxies are bright enough to permit accurate pixel-by-pixel k-corrections into the restframe UV (∼ 2000 Å). 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. In addition, an estimate of 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 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 ∼ 0.5 population. By simple image transformations we demonstrate that bolometric luminosity evolution generates galaxies which are too large and the contribution of any