Getting more out of V/Vm than just the mean

TL;DR

This paper applies a procedure to derive the cosmological number density n(z) from the fractional volume distribution V/Vm using a larger quasar sample, providing insights into redshift distribution and luminosity functions.

Contribution

It extends Banhatti's method to a larger quasar sample, enabling detailed analysis of n(z) and redshift distribution from V/Vm data.

Findings

Derived n(z) for 8 redshift values up to 3.5

Linked n(z) to the radio luminosity function { ho}(P, z)

Provided a method to analyze quasar distributions using V/Vm

Abstract

Banhatti (2009) set down the procedure to derive cosmological number density n(z) from the differential distribution p(x) of the fractional luminosity volume relative to the maximum volume, x \equiv V/Vm (0 \leq x \leq 1), using a small sample of 76 quasars for illustrative purposes. This procedure is here applied to a bigger sample of 286 quasars selected from Parkes half-Jansky flat-spectrum survey at 2.7 GHz (Drinkwater et al 1997). The values of n(z) are obtained for 8 values of redshift z from 0 to 3.5. The function n(z) can be interpreted in terms of redshift distribution obtained by integrating the radio luminosity function {\rho}(P, z) over luminosities P for the survey limiting flux density S0 = 0.5 Jy. Keywords. V/Vm - luminosity-volume - cosmological number density - redshift distribution - luminosity function - quasars [Note: This somewhat modified version was submitted to MNRaS on 14 July 2016. It was (almost) rejected, except if thoroughly revised.]