Standard and Truncated Luminosity Functions for stars in the Gaia Era

TL;DR

This paper models stellar luminosity functions using Schechter and Gamma distributions, incorporating boundaries to account for observational biases, and demonstrates applications in astrophysics such as bias correction and parameter estimation.

Contribution

It introduces truncated Schechter and Gamma luminosity functions for stars, addressing observational boundaries and Malmquist bias in the Gaia era.

Findings

Effective modeling of star luminosity functions with boundaries.

Application to Malmquist bias correction.

Insights into star brightness distribution with distance.

Abstract

The luminosity function (LF) for stars is here fitted by a Schechter function and by a Gamma probability density function. The dependence of the number of stars on the distance, both in the low and high luminosity regions, requires the inclusion of a lower and upper boundary in the Schechter and Gamma LFs. Three astrophysical applications for stars are provided: deduction of the parameters at low distances, behavior of the average absolute magnitude with distance, and the location of the photometric maximum as a function of the selected flux. The use of the truncated LFs allows to model the Malmquist bias.