Constraints on the Thomson optical depth to the Cosmic Microwave Background from the Lyman- α forest

We present the first constraints on the electron optical depth to reionization, τe, from the Lyman-α forest alone for physically motivated reionization models that match the reionization's end point, zend, required by the same astrophysical probe, and for symmetric reionization models with fixed duration, Δz, commonly adopted in cosmic microwave background (CMB) reionization analyses. Compared to traditional estimates from the latter, the Lyman-α forest traces the ionization state of the Intergalactic medium (IGM) through its coupling with the thermal state. We find an explicit mapping between the two by solving the chemistry and temperature evolution equations for hydrogen and helium. Our results yield τe = 0.040-0.018+0.042 (95% C.L.) and τe = 0.041-0.017+0.028 for reionization models with zend and Δz fixed, respectively. With mock Lyman-α forest data that mimics the precision of future larger quasar sample datasets, we would potentially obtain tighter τe constraints, paving the way for CMB-independent constraints on the epoch of reionization from a large-scale structure probe.