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-Re) distribution. With a careful analysis of selection effects due to both detection completeness and measurement reliability we identify bias-free regions in the M-Re 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 ~ 0.7. Specifically, we demonstrate that the mean, rest-frame B-band surface brightness for galaxies in a sample spanning 8 magnitudes in luminosity between M = -22 and -14 mag increases by ~1.0 mag/arcsec^2 from z ~ 0.1 to z ~ 0.7. We also highlight the importance of considering surface brightness dependent measurement biases in addition to incompleteness biases. In particular, the increasing, systematic under-estimation of Kron fluxes towards low surface brightnesses may cause diffuse, yet luminous, systems to be mistaken for faint, compact objects.