2009MNRAS.397..868S

We present luminosity and surface-brightness distributions of 40111 galaxies with K-band photometry from the United Kingdom Infrared Telescope (UKIRT) Infrared Deep Sky Survey (UKIDSS) Large Area Survey (LAS), Data Release 3 and optical photometry from Data Release 5 of the Sloan Digital Sky Survey (SDSS). Various features and limitations of the new UKIDSS data are examined, such as a problem affecting Petrosian magnitudes of extended sources. Selection limits in K- and r-band magnitude, K-band surface brightness and K-band radius are included explicitly in the 1/V_maxestimate of the space density and luminosity function. The bivariate brightness distribution in K-band absolute magnitude and surface brightness is presented and found to display a clear luminosity-surface brightness correlation that flattens at high luminosity and broadens at low luminosity, consistent with similar analyses at optical wavelengths. Best-fitting Schechter function parameters for the K-band luminosity function are found to be M* - 5 logh = -23.19±0.04,α = -0.81±0.04 and φ* = (0.0166±0.0008)h³Mpc^–3, although the Schechter function provides a poor fit to the data at high and low luminosity, while the luminosity density in the K band is found to be j = (6.305±0.067)x10⁸L_☉hMpc^–3. However, we caution that there are various known sources of incompleteness and uncertainty in our results. Using mass-to-light ratios determined from the optical colours, we estimate the stellar mass function, finding good agreement with previous results. Possible improvements are discussed that could be implemented when extending this analysis to the full LAS.