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

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Abstract
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 sq deg and probing approximately one--two mag/sq arcsec 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 B_mgc < 20 mag with 96 per cent spectroscopic completeness. 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_{B}* - 5 log h = (-19.60 +/- 0.04) mag and alpha =-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 j_{b_J} = (1.99 +/- 0.17) x 10^8 h L_{odot} Mpc^{-3}. 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/sq arcsec and sigma_{ln R_e} = 0.35 +/- 0.01. The characteristic surface brightness for luminous systems is invariant to M_{B} - 5 log h ~ -19 mag faintwards of which it moves to lower surface brightness. Higher resolution (FWHM < 1 arcsec) and deeper (mu_eff > 26 mag/sq arcsec in the B-band) observations of the local universe are now essential to probe to lower luminosity and lower surface brightness levels. [abridged]

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