A New Boundary Condition on Reionization

Abstract: The epoch of reionization (EoR) marks the last phase transition of hydrogen in our Universe, as it evolves from cold and neutral to hot and ionized in the intergalactic medium (IGM). While its endpoint and duration can be estimated from current observations, albeit with large uncertainties, there is no known avenue to constrain its onset. We propose a novel method based on the Pearson cross-correlation coefficient between 21-cm brightness temperature maps and line-intensity maps tracing star-formation (e.g., OIII, CO, CII). This real-space estimator evolves from negative to positive as X-ray heating progresses, and saturates prior to the EoR. We predict a sharp turnover from saturation during the earliest EoR stages, when the IGM ionized fraction reaches $\bar{x}_{\rm HII}\sim 1\%-10\%$. We show that in standard scenarios, where the IGM heating precedes reionization, the turnover is a clear, model-robust signature. Its detection will provide a unique observational anchor for the EoR onset, complementing existing probes and tightening constraints on early galaxy formation models.