A quick estimation of luminosity function based on the luminosity-distance diagram

TL;DR

This paper introduces a rapid method to estimate the luminosity function of astrophysical objects using the luminosity-distance diagram, which does not require complete samples and assumes uniform spatial distribution.

Contribution

The paper presents a novel, efficient approach to determine luminosity functions from luminosity-distance data without complete sampling, applicable to simulated and real data.

Findings

Method accurately estimates luminosity function in simulations

Does not require complete sample data

Applicable to energy functions as well

Abstract

Based on the luminosity-distance diagram, we propose a method to quickly estimate the luminosity function for any certain astrophysical objects. Giving the mean distance between any two objects at a given luminosity range, we can find the relation between the mean distance and the luminosity, and consequently can obtain the luminosity function. Not like the straightforward counting method, this method does not need a complete sample. The only requirement is that the object distributes uniformly in space. We apply this method to a simulated sample, and find it can produce the luminosity function properly. This method can also be used for energy function.