The Millennium Galaxy Catalogue: the space density and surface brightness distribution(s) of galaxies

We recover the joint and individual space density and surface brightness distribution(s) of galaxies from the Millennium Galaxy Catalogue. The MGC is a local survey spanning 30.9 deg and probing approximately one–two mag arcsec deeper than either the TwoDegree Field Galaxy Redshift Survey (2dFGRS) or the Sloan Digital Sky Survey (SDSS). The MGC contains 10 095 galaxies to BMGC < 20 mag with 96 per cent spectroscopic completeness. For each galaxy we derive individual K-corrections and seeing-corrected sizes. We implement a joint luminosity-surface brightness step-wise maximum likelihood method to recover the bivariate brightness distribution (BBD) inclusive of most selection effects. Integrating the BBD over surface brightness we recover the following Schechter function parameters: φ = (0.0177 ± 0.0015)h Mpc, M BMGC − 5 logh = (−19.60 ± 0.04) mag and α = −1.13 ± 0.02. Compared to the 2dFGRS (Norberg et al. 2002) we find a consistent M value but a slightly flatter faint-end slope and a higher normalisation, resulting in a final luminosity density jbJ = (1.99 ± 0.17) × 10 8 hL⊙ Mpc — marginally higher than, but consistent with, the earlier 2dFGRS (Norberg et al. 2002), ESP (Zucca et al. 1997), and SDSS z = 0.1 (Blanton et al. 2003a) results. The MGC is inconsistent with the SDSS z = 0 result (+3σ) if one adopts the derived SDSS evolution (Blanton et al. 2003a). The MGC surface brightness distribution is a well bounded Gaussian at the M point with φ = (3.5 ± 0.1) × 10h Mpc, μ = (21.90 ± 0.01) mag arcsec and σln Re = 0.35 ± 0.01. The characteristic surface brightness for luminous systems is invariant to MBMGC − 5 logh ≈ −19 mag faintwards of which it moves to lower surface brightness. The surface brightness distribution also broadens (σlnRe ≈ 0.5 − 0.7) towards lower luminosities. The luminosity dependence of σln Re provides a new constraint for both the theoretical development (Dalcanton, Spergel & Summers 1997; Mo, Mao & White 1998) and numerical simulations (e.g., Cole & Lacey 1996) which typically predict a mass-independent σln Re ≈ 0.56 ± 0.04 (see Vitvitska et al. 2002 and Bullock et al. 2001). Higher resolution (FWHM ≪ 1 arcsec) and deeper (μLIM ≫ 26 mag arcsec in the Bband) observations of the local universe are now essential to probe to lower luminosity and lower surface brightness levels.