A New Luminosity Function for Galaxies as Given by the Mass-Luminosity Relationship

Abstract

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.

New formulas for the Hubble constant in a Euclidean static universe

“…This value lies between the value deduced from the Cepheids, see Sandage et al [13] and formula (3) and the value deduced from WMAP, see Spergel et al [14] and formula (4). The developed framework also enables the deduction of the reference magnitude of the sun, see formula (29) and the application to the 2dFGRS gives M ⊙ = (5.5 ± 0.35) .…”

“…Numerical values of the Hubble constant as deduced from 10 different apparent magnitudes.The reference absolute magnitude of the sun (the unknown variable) can be derived from formula(29) but in this case the value of H 0 (known variable) should be specified. Perhaps the best choice is the weighted mean reported inTable (1), H 0 = 66.04 km s −1 Mpc −1 .…”

New Probability Distributions in Astrophysics: I. The Truncated Generalized Gamma

“…The above line of research allows exploring the LF for galaxies in the framework of well studied PDFs. Some examples are represented by the mass-luminosity relationship, see [9], some models connected with the generalized gamma (GG) distribution, see [10,11], the truncated beta LF, see [12], the lognormal LF, see [13], the truncated lognormal LF, see [14], and the Lindley LF, see [15]. This paper brings up the GG and introduces the scale in Section 2.…”

A Lognormal Luminosity Function for SWIRE in Flat Cosmology

“…A first improvement for the standard LF can be obtained from a given probability density function (PDF) (i.e. the gamma variate) for the mass of the galaxies, M, and by assuming a non-linear relationship between M and luminosity (L), see [14]. A second improvement analyzes standard PDFs, such as the generalized gamma, and then converts it to a LF, see [15].…”