Precise Measurement of the Reionization Optical Depth from The Global 21-cm Signal Accounting for Cosmic Heating

As a result of our limited data on reionization, the total optical depth for electron scattering, $\tau$, limits precision measurements of cosmological parameters from the Cosmic Microwave Background (CMB). It was recently shown that the predicted 21-cm signal of neutral hydrogen contains enough information to reconstruct $\tau$ with sub-percent accuracy, assuming that the neutral gas was much hotter than the CMB throughout the entire epoch of reionization. Here we relax this assumption and use the global 21-cm signal alone to extract $\tau$ for realistic X-ray heating scenarios. We test our model-independent approach using mock data for a wide range of ionization and heating histories and show that an accurate measurement of the reionization optical depth at a sub-percent level is possible in most of the considered scenarios even when heating is not saturated during the epoch of reionization, assuming that the foregrounds are mitigated. However, we find that in cases where heating sources had hard X-ray spectra and their luminosity was close to or lower than what is predicted based on low-redshift observations, the global 21-cm signal alone is not a good tracer of the reionization history.