The galaxy luminosity-size relation and selection biases in the Hubble Ultra Deep Field

We use the Hubble Ultra Deep Field to study the galaxy luminosity-size (M-R-e) distribution. With a careful analysis of selection effects due to both detection completeness and measurement reliability, we identify bias-free regions in the M-R-e plane for a series of volume-limited samples. By comparison to a nearby survey also having well-defined selection limits, namely the Millennium Galaxy Catalogue, we present clear evidence for evolution in surface brightness since z similar to 0.7. Specifically, we demonstrate that the mean, rest-frame B-band (e) for galaxies in a sample spanning 8 mag in luminosity between M-B = -22 and -14 mag increases by similar to 1.0 mag arcsec(-2) from z similar to 0.1 to 0.7. We also highlight the importance of considering surface brightness-dependent measurement biases in addition to incompleteness biases. In particular, the increasing, systematic underestimation of Kron fluxes towards low surface brightnesses may cause diffuse, yet luminous, systems to be mistaken for faint, compact objects.