Analysis of a complete galaxy redshift survey - II. The field-galaxy luminosity function

We present a detailed analysis of the field-galaxy luminosity function for five magnitude-limited redshift surveys. We apply maximum-likelihood estimators which we demonstrate provide unbiased estimates of the luminosity function for spatially inhomogeneous distributions under the assumption that luminosity is uncorrelated with position. A likelihood-ratio test is devised which can be used to assess whether specific functional forms of the luminosity function provide acceptable fits to the observations. These methods, and asymptotic estimates of their errors, are checked against Monte Carlo simulations. Our results show that the luminosity functions from the AARS, KOS and KOSS redshift surveys are all compatible with Schechter functions. The luminosity function for the CfA survey does not fit a Schechter function. In particular, the bright end falls off less steeply than a Schechter function, but we argue that this is caused by the large random errors in the Zwicky magnitudes. From these field surveys there is no evidence for morphological type differences in the field luminosity function for types earlier than Sc. Later type galaxies (Sc-I) are significantly fainter than earlier types. With the exception of the CfA survey, the luminosity functions derived from the redshift surveys are compatible with each other. We conclude that the field luminosity function is well described by a Schechter function with parameters $$\alpha=-1.07\pm0.05,M{^\ast_B}_\text T=-19.68\pm0.10, \enspace\text{and}\enspace\phi^\ast=(1.56\pm0.34)\times10^{-2}\text {Mpc} ^{-3}\enspace \text{for}\enspace H_0=100 \text{km}\text s^{-1}\text {Mpc} ^{-2}$$.