We recover the joint and individual space density and surface-brightness distribution(s) of galaxies from the Millennium Galaxy Catalogue (MGC). The MGC is a local survey spanning 30.9 deg2 and probing approximately 1–2 mag arcsec−2 deeper than either the Two-Degree 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) h3 Mpc−3, M*− 5 log h= (−19.60 ± 0.04) mag and α=−1.13 ± 0.02. Compared to the 2dFGRS we find a consistent M* value but a slightly flatter faint-end slope and a higher normalization, resulting in a final luminosity density j= (1.99 ± 0.17) × 108 h L⊙ Mpc−3– marginally higher than, but consistent with, the earlier 2dFGRS, ESP, and SDSS z= 0.1 results. The MGC is inconsistent with the SDSS z= 0.0 result (+3σ) if one adopts the derived SDSS evolution.
The MGC surface-brightness distribution is a well-bounded Gaussian at the M* point with φ*= (3.5 ± 0.1) × 10−2h3 Mpc−3, μe*= (21.90 ± 0.01) mag arcsec−2 and σ= 0.35 ± 0.01. The characteristic surface brightness for luminous systems is invariant to M− 5 log h≈−19 mag faintwards of which it moves to lower surface brightness. The surface-brightness distribution also broadens (σ≈ 0.5 − 0.7) towards lower luminosities. The luminosity dependence of σln Re provides a new constraint for both the theoretical development and numerical simulations, which typically predict a mass-independent σ≈ 0.56 ± 0.04.
Higher resolution (FWHM ≪ 1 arcsec) and deeper (μlim≫ 26 mag arcsec−2 in the B-band) observations of the local Universe are now essential to probe to lower luminosity and lower surface-brightness levels.