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 deg(2) 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 (BBD) inclusive of most selection effects. Integrating the BBD over surface brightness we recover the following Schechter function parameters: phi* = (0.0177 +/- 0.0015) h(3) Mpc(-3), M*(BMGC) - 5 log h =(-19.60 +/- 0.04) mag and alpha = -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(bJ) = (1.99 +/- 0.17) x 10(8) h L-circle dot 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 (+3 sigma) if one adopts the derived SDSS evolution. The MGC surface-brightness distribution is a well-bounded Gaussian at the M* point with phi* = (3.5 +/- 0.1) x 10(-2) h(3) Mpc(-3), mu(e)* = (21.90 +/- 0.01) mag arcsec(-2) and sigma(InRe) = 0.35 +/- 0.01. The characteristic surface brightness for luminous systems is invariant to M-BMGC - 5 log h approximate to -19 mag faintwards of which it moves to lower surface brightness. The surface-brightness distribution also broadens (sigma(InRe) approximate to 0.5 - 0.7) towards lower luminosities. The luminosity dependence of sigma(InRe) provides a new constraint for both the theoretical development and numerical simulations, which typically predict a mass-independent sigma(InRe) approximate to 0.56 +/- 0.04. Higher resolution (FWHM << 1 arcsec) and deeper (mu(Iim) >> 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.