Quantifying the Precision of IGM Damping Wing Measurements Towards Quasars

We investigate the precision with which the Lyman-$\alpha$ damping wing signature imprinted on the spectra of high-redshift quasars (QSOs) by the foreground neutral intergalactic medium (IGM) can measure the history of cosmic reionization. We leverage a novel inference pipeline based on a generative probabilistic model for the entire spectrum (both red- and blueward of the Lyman-$\alpha$ line), accounting for all relevant sources of uncertainty - the stochasticity caused by patchy reionization, the impact of the quasar's ionizing radiation on the IGM, it's unknown intrinsic spectrum, and spectral noise. Performing fast JAX-based Hamiltonian Monte-Carlo (HMC) parameter inference, we precisely measure the underlying global IGM neutral fraction as well as the lifetime of the quasar. Running a battery of tests on over a thousand mocks, we find optimal precision when running the pipeline with a six parameter PCA continuum model (five coefficients and a normalization) on $\mathrm{S}/\mathrm{N} \sim 10$ spectra, binned to a $\sim 500\,\mathrm{km}/\mathrm{s}$ velocity pixel scale, and extending at least out to the C IV $\lambda\,1549\,\text{\r{A}}$ emission line. After marginalizing out nuisance parameters associated with the quasar continuum, a single spectrum constrains the IGM neutral fraction to $28.0_{-8.8}^{+8.2}\,\%$ and the quasar lifetime to $0.80_{-0.55}^{+0.22}\,\mathrm{dex}$, improving notably towards spectra with a stronger IGM damping wing imprint. Higher precision can be achieved by averaging over statistical quasar samples. We identify two primary sources of uncertainty that contribute approximately equally to the total error budget: the uncertain quasar continuum model and the stochastic distribution of neutral regions arising from both the reionization topology and the location of the quasar's ionization front.