Quasar Ionization Front Ly{\alpha} Emission in an Inhomogeneous Intergalactic Medium

The conditions within the ionization front of a quasar during reionization (T ~ 30,000 K, neutral hydrogen fraction ~ 0.5) are ideal for producing Lyman-alpha emission via collisional excitation of hydrogen atoms. Observations of this emission, which could subtend >10 arcmin$^2$ on the sky, would definitively demonstrate the presence of a neutral intergalactic medium at the observed epoch, placing valuable constraints on the progress of reionization. We find that the expected Lyman-alpha surface brightness is significantly weaker than previously determined and may be impossible to observe with current and near-future instruments. Past work calculated the Lyman-alpha emission from a quasar ionization front in a homogeneous medium with a clumping factor approximation to account for inhomogeneities. We find using 1D radiative transfer calculations that this approximation overestimates the emission by a factor of >3. Our calculations model the propagation of ionizing photons and compute the Lyman-alpha emission from quasar ionization fronts on sightlines from a hydrodynamic cosmological simulation at z = 7.1. To better understand the physical properties of the emission, we also develop an analytic model that accurately describes the results of the full radiative transfer calculation.