Fully probabilistic quasar continua predictions near Lyman-{\alpha} with conditional neural spline flows

Measurement of the red damping wing of neutral hydrogen in quasar spectra provides a probe of the epoch of reionization in the early Universe. Such quantification requires precise and unbiased estimates of the intrinsic continua near Lyman-$\alpha$ (Ly$\alpha$), a challenging task given the highly variable Ly$\alpha$ emission profiles of quasars. Here, we introduce a fully probabilistic approach to intrinsic continua prediction. We frame the problem as a conditional density estimation task and explicitly model the distribution over plausible blue-side continua ($1190\ \unicode{xC5} \leq \lambda_{$\text{rest}$} < 1290\ \unicode{xC5}$) conditional on the red-side spectrum ($1290\ \unicode{xC5} \leq \lambda_{$\text{rest}$} < 2900
\unicode{xC5}$) using normalizing flows. Our approach achieves state-of-the-art precision and accuracy, allows for sampling one thousand plausible continua in less than a tenth of a second, and can natively provide confidence intervals on the blue-side continua via Monte Carlo sampling. We measure the damping wing effect in two $z>7$ quasars and estimate the volume-averaged neutral fraction of hydrogen from each, finding ${\bar{x}}_{\text{HI}}=0.304\pm 0.042$ for ULAS J1120+0641 ($z=7.09$) and ${\bar{x}}_{\text{HI}}=0.384\pm 0.133$ for ULAS J1342+0928 ($z=7.54$).