Effect of spectral index distribution on estimating the AGN radio luminosity function

TL;DR

This study investigates how the distribution of spectral indices affects the estimation of the AGN radio luminosity function, revealing biases in traditional methods and proposing a new trivariate approach for more accurate measurements.

Contribution

The paper introduces a trivariate function incorporating spectral index, redshift, and luminosity to improve AGN RLF estimation accuracy.

Findings

Traditional bivariate estimators cause bias, especially for flat-spectrum sources.

Spectral index distribution impacts the accuracy of RLF estimates.

A new trivariate function provides a more robust measurement of the RLF.

Abstract

In this paper, we scrutinize the effect of spectral index distribution on estimating the AGN (active galactic nucleus) radio luminosity function (RLF) by a Monte Carlo method. We find that the traditional bivariate RLF estimators can cause bias in varying degree. The bias is especially pronounced for the flat-spectrum radio sources whose spectral index distribution is more scattered. We believe that the bias is caused because the $K$-corrections complicate the truncation boundary on the $L-z$ plane of the sample, but the traditional bivariate RLF estimators have difficulty in dealing with this boundary condition properly. We suggest that the spectral index distribution should be incorporated into the RLF analysis process to obtain a robust estimation. This drives the need for a trivariate function of the form $\Phi(\alpha,z,L)$ which we show provides an accurate basis for measuring the RLF.