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