Ultraviolet background fluctuations with clustered sources

TL;DR

This paper develops a mathematical framework to model ultraviolet background fluctuations considering source clustering, applying it to helium reionization and quasar distributions, revealing clustering's limited impact on intensity variance under certain conditions.

Contribution

It introduces an exact count-in-cells formalism incorporating source clustering via the hierarchical ansatz, linking intensity distribution solely to the 2-point correlation function.

Findings

Quasar clustering contributes less than 30% to intensity fluctuation variance for certain attenuation lengths.

Void scaling function of high redshift quasars aligns with the Negative Binomial distribution.

Environmental density affects the mean HeII-ionizing intensity, with potential differences of a factor of a few.

Abstract

We develop a count-in-cells approach to the distribution of ultraviolet background fluctuations that includes source clustering. We demonstrate that an exact expression can be obtained if the clustering of ionizing sources follows the hierarchical ansatz. In this case, the intensity distribution depends solely on their 2-point correlation function. We show that the void scaling function of high redshift mock quasars is consistent with the Negative Binomial form, before applying our formalism to the description of HeII-ionizing fluctuations at the end of helium reionization. The model inputs are the observed quasar luminosity function and 2-point correlation at redshift $z\sim 3$. We find that, for an (comoving) attenuation length $\lesssim $ 55 Mpc, quasar clustering contributes less than 30% of the variance of intensity fluctuations so long as the quasar correlation length does not exceed 15 Mpc. We investigate also the dependence of the intensity distribution on the large-scale environment. Differences in the mean HeII-ionizing intensity between low- and high-density regions could be a factor of few if the sources are highly clustered. An accurate description of quasar demographics and their correlation with strong absorption systems is required to make more precise predictions.