The 2dF Galaxy Redshift Survey: the b(J)-band galaxy luminosity function and survey selection function

We use more than 110 500 galaxies from the 2dF Galaxy Redshift Survey (2dFGRS) to estimate the b(J)-band galaxy luminosity function at redshift z = 0, taking account of evolution, the distribution of magnitude measurement errors and small corrections for incompleteness in the galaxy catalogue. Throughout the interval -16.5 > M-bJ 5 log(10) h > -22, the luminosity function is accurately described by a Schechter function with M-bJ* - 5 log(10) h = -19 66 +/- 0 07, alpha = -1.21 +/- 0.03 and Phi* = (1.61 +/- 0.08) x 10-(2) h(3) Mpc(-3), giving an integrated luminosity density of rho(L) = (1.82 +/- 0.17) x 10(8) h L. Mpc(-3) (assuming an Omega(0) = 0.3, Lambda(0) = 0.7 cosmology). The quoted errors have contributions from the accuracy of the photometric zero-point, from large-scale structure in the galaxy distribution and, importantly, from the uncertainty in the appropriate evolutionary corrections. Our luminosity function is in excellent agreement with, but has much smaller statistical errors than, an estimate from the Sloan Digital Sky Survey (SDSS) data when the SDSS data are accurately translated to the b(J) band and the luminosity functions are normalized in the same way. We use the luminosity function, along with maps describing the redshift completeness of the current 2dFGRS catalogue, and its weak dependence on apparent magnitude, to define a complete description of the 2dFGRS selection function. Details and tests of the calibration of the 2dFGRS photometric parent catalogue are also presented.