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 - 5 { \log _ { 10 } h } > -22 , the luminosity function is accurately described by a Schechter function with M ^ { \star } _ { b _ { J } } -5 { \log _ { 10 } h } = -19.66 \pm 0.07 , \alpha = -1.21 \pm 0.03 and \Phi ^ { \star } = ( 1.61 \pm 0.08 ) \times 10 ^ { -2 } h ^ { 3 } Mpc ^ { -3 } , giving an integrated luminosity density of \rho _ { L } = ( 1.82 \pm 0.17 ) \times 10 ^ { 8 } h L _ { \odot } Mpc ^ { -3 } ( assuming an \Omega _ { 0 } = 0.3 , \Lambda _ { 0 } = 0.7 cosmology ) .
The quoted errors have contributions from the accuracy of the photometric zeropoint , 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 .