# Large-scale fluctuations in the cosmic ionising background: the impact of beamed source emission

## TL;DR

This paper investigates how beamed emission from quasars affects large-scale fluctuations in the cosmic ionising background, revealing that beaming can alter the power spectrum and impact interpretations of observational data.

## Contribution

It introduces a model incorporating source beaming into ionisation fluctuation calculations, highlighting its effects on the power spectrum and shot-noise contributions.

## Key findings

- Beaming partially cancels effects on the power spectrum at certain scales.
- Source density renormalisation can significantly reduce shot-noise contributions.
- Beaming effects are important for interpreting future observational data.

## Abstract

When modelling the ionisation of gas in the intergalactic medium after reionisation, it is standard practice to assume a uniform radiation background. This assumption is not always appropriate; models with radiative transfer show that large-scale ionisation rate fluctuations can have an observable impact on statistics of the Lyman-alpha forest. We extend such calculations to include beaming of sources, which has previously been neglected but which is expected to be important if quasars dominate the ionising photon budget. Beaming has two effects: first, the physical number density of ionising sources is enhanced relative to that directly observed; and second, the radiative transfer itself is altered. We calculate both effects in a hard-edged beaming model where each source has a random orientation, using an equilibrium Boltzmann hierarchy in terms of spherical harmonics. By studying the statistical properties of the resulting ionisation rate and HI density fields at redshift $z\sim 2.3$, we find that the two effects partially cancel each other; combined, they constitute a maximum $5\%$ correction to the power spectrum $P_{\mathrm{HI}}(k)$ at $k=0.04 \, h/\mathrm{Mpc}$. On very large scales ($k<0.01\, h/\mathrm{Mpc}$) the source density renormalisation dominates; it can reduce, by an order of magnitude, the contribution of ionising shot-noise to the intergalactic HI power spectrum. The effects of beaming should be considered when interpreting future observational datasets.