Magnification Effects on Source Counts and Fluxes

TL;DR

This paper develops a framework to quantify how sky-varying gravitational lensing magnification affects observed source counts and fluxes, with applications to high-redshift galaxy observations and SZ measurements.

Contribution

It provides new expressions linking magnification probability distributions to observed counts and fluxes, clarifying previous conflicting results and enabling precise calculations of magnification effects.

Findings

Lensing causes significant scatter in SZ observations at high frequencies.

High-luminosity galaxy counts are enhanced and follow a power-law distribution due to magnification.

The framework can be applied to various astrophysical scenarios involving magnification effects.

Abstract

We consider the effect of lensing magnification on high redshift sources in the case that magnification varies on the sky, as expected in wide fields of view or within observed galaxy clusters. We give expressions for number counts, flux and flux variance as integrals over the probability distribution of the magnification. We obtain these through a simple mapping between averages over the observed sky and over the magnification probability distribution in the source plane. Our results clarify conflicting expressions in the literature and can be used to calculate a variety of magnification effects. We highlight two applications: 1. Lensing of high-z galaxies by galaxy clusters can provide the dominant source of scatter in SZ observations at frequencies larger than the SZ null. 2. The number counts of high-z galaxies with a Schechter-like luminosity function will be changed at high luminosities to a power law, with significant enhancement of the observed counts at L > 10 L*.