Direct construction of the galaxy luminosity function as a function of redshift

This paper describes a new method for investigating the evolution of the galaxy luminosity function using the results of faint galaxy redshift surveys. In this method the luminosity function is calculated at a number of redshifts using the PHIG_ estimator of Felten, and the errors on the luminosity function are estimated using the spatial correlation function. Compared with the standard method used for analyzing the redshift survey results, this method has a number of advantages: all the information present in a redshift survey, magnitudes as well as redshifts, is used; there is no need to bin galaxies into morphological classes; and there is no ambiguity about analyzing the results of more than two redshift surveys. The most important advantage of the new method, however, is that while the standard method merely gives a yes/no decision about whether a particular model is an adequate fit to the data. the result of applying the new method is an immediate pictorial impression, as well as a direct quantitative measure, of both the strength and type of evolution and of the limitations of the data. This method was applied to three recent redshift surveys with the following results. There is strong evidence that the amplitude of the luminosity function increases by a large factor (3) in the redshift range 0 < Z < 0. 4, while there is no evidence for any change in the shape of the luminosity function. There is also evidence in the redshift data for an increase in the amplitude of the luminosity function at a redshift of only ~0. 15-0. 2, supporting the inference of Maddox et al. (1990b) from the APM galaxy survey results that the luminosity function must show evolution at a very low redshift. The strength of this low-redshift evolution is, however, poorly constrained by the redshift surveys. The galaxy number counts and the results of the new analysis were used to investigate the explanations that have been suggested for the observed evolution. The number counts are inconsistent with models that are based on the passive evolution of the current stellar populations of galaxies. and using a nonzero cosmological constant is little help. The fact that the amplitude but not the shape of the luminosity function shows strong evolution is evidence against models based on merging. Only starburst models seem consistent with the observations. The main uncertainty in the starburst models is the shape of the dwarf luminosity function in the field. If this is assumed to have the same shape as the dwarf luminosity function in the Virgo cluster, then to be consistent with the observations, almost all dwarf galaxies, and only dwarf galaxies, have to be undergoing starbursts at z ~ 0. 15-0. 4. If the dwarf luminosity function, however, is similar in shape to the low-luminosity end of the luminosity function found here, it is possible to fit the observations with a less extreme model, in which all galaxies have an enhanced, but moderate (~6%), probability of being in a starburst phase at z ~ 0. 15-0. 4. Subject headings cosmology: observations - galaxies: distances and redshifts - galaxies: fundamental parameters