A new luminosity function for galaxies as given by the mass-luminosity relationship

The search for a luminosity function for galaxies both alternative or companion to a Schechter function is a key problem in the reduction of data from catalogs of galaxies. Two luminosity functions for galaxies can be built starting from two distributions of mass as given by the fragmentation. A first overall distribution function is the Kiang function, which represents a useful description of the area and volume distribution of the Poisson Voronoi diagrams. The second distribution, which covers the case of low-mass galaxies, is the truncated Pareto distribution: in this model we have a natural bound due to the minimum mass/luminosity observed and an upper bound (function of the considered environment) represented by the boundary with the observed mass/luminosity overall behavior. The mass distribution is then converted into a luminosity distribution through a standard mass–luminosity relationship. The mathematical rules to convert the probability density function are used and the two new functions are normalized to the total number of galaxies per unit volume. The test of the two new luminosity functions for galaxies that cover different ranges in magnitude was made on the Sloan Digital Sky Survey (SDSS) in five different bands; the results are comparable to those of the Schechter function. A new parameter, which indicates the stellar content, is derived. The joint distribution in redshift and flux, the mean redshift and the number density connected with the first luminosity function for galaxies are obtained by analogy with the Schechter function. A new formula, which allows us to express the mass as a function of the absolute magnitude, is derived.