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 (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 10095 galaxies to B_MGC < 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 (BED) inclusive of most selection effects. Integrating the BED over surface brightness we recover the following Schechter function parameters: φ* = (0.0177 ± 0.0015) h^-3 Mpc^-3, M*_BMGC - 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 jb_bj = (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, μ ^e* = (21.90 ± 0.01) mag arcsec⁺² and σ_lnRe = 0.35 ± 0.01. The characteristic surface brightness for luminous systems is invariant to M_BMGC - 5 log h ≈ -19 mag faintwards of which it moves to lower surface brightness. The surface-brightness distribution also broadens (σ_lnRe 0.5 - 0.7) towards lower luminosities. The luminosity dependence of σ _lnRe provides a new constraint for both the theoretical development and numerical simulations, which typically predict a mass-independent σ_lnRe≈ 0.56 ± 0.04. Higher resolution (FWHM ≪ 1 arcsec) and deeper (μ_lim ≫ 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.