On the product of two gamma variate with argument 2: Application to the luminosity function for galaxies

TL;DR

This paper introduces a new galaxy luminosity function based on the product of two gamma variates, compares it with existing models, and tests its applicability using SDSS data across multiple bands.

Contribution

It derives a novel galaxy luminosity function from the product of two gamma variates and applies it to SDSS data, offering an alternative to the Schechter function.

Findings

The new luminosity function is mathematically characterized, including mean and distribution.

It is tested against SDSS data in five bands, showing less accuracy than the Schechter function.

The derived functions provide a new perspective on galaxy mass and luminosity distribution.

Abstract

A new luminosity function for galaxies can be built starting from the product of two random variables X and Y represented by a gamma variate with argument 2 >. The mean, the standard deviation and the distribution function of this new distribution are computed. This new probability density function is assumed to describe the mass distribution of galaxies. Through a non linear rule of conversion from mass to luminosity a second new luminosity function for galaxies is derived. The test of reliability of these two luminosity functions was made on the Sloan Digital Sky Survey (SDSS) in five different bands. The Schechter function gives a better fit with respect to the two new luminosity functions for galaxies here derived.