The K-band luminosity function at z=1: a powerful constraint on galaxy formation theory

There are two major approaches to modelling galaxy evolution. The traditional view is that the most massive galaxies were assembled early and have evolved with steeply declining star formation rates since a redshift of 2 or higher. According to hierarchical theories, massive galaxies were assembled much more recently from mergers of smaller subunits. Here we present a simple observational test designed to differentiate between the two. The observed K-band flux from a galaxy is a good measure of its stellar mass even at high redshift. It is probably only weakly affected by dust extinction. We compute the evolution of the observed K-band luminosity function for traditional, pure luminosity evolution (PLE) models and for hierarchical models. At z=0, both models can fit the observed local K-band luminosity function. By redshift 1, they differ greatly in the predicted abundance of bright galaxies. We calculate the redshift distributions of K-band selected galaxies and compare these with available data. We show that the number of K<19 galaxies with redshifts greater than 1 is well below the numbers predicted by the PLE models. In the Songaila et al (1994) redshift sample of 118 galaxies with 16<K<18, 33 galaxies are predicted to lie at z>1. Only 2 are observed. In the Cowie et al. (1996) redshift sample of 52 galaxies with 18<K<19, 28 galaxies are predicted to lie at at z>1. Only 5 are observed. Both these samples are more than 90% complete. We conclude that there is already strong evidence that the abundance of massive galaxies at z=1 is well below the local value. This is inconsistent with the traditional model, but similar to the expectations of hierarchical models.