The Future of Gamma-Ray Bursts as Probes of the Epoch of Reionization in the Era of JWST and the Extremely Large Telescope

The Epoch of Reionization (EoR) is a key era of cosmological history that remains poorly understood. An examination of the Ly-alpha damping wing of high-redshift GRBs can provide direct measurements of the fraction of neutral hydrogen (i.e., neutral fraction) of the IGM in the vicinity of the GRB host galaxy, in addition to the neutral column in the host along the sight-line to the GRB. The latter quantity can help infer the fraction of ionizing photons escaping the galaxy (i.e. escape fraction); the average escape fraction being a key input to EoR models. New and upcoming observatories such as the JWST and the Extremely Large Telescope (ELT) can obtain more robust estimates of the hydrogen column density and neutral fraction around high-redshift GRBs. We simulate spectra for the JWST NIRSpec and ELT HARMONI spectrographs using different GRB magnitudes and exposure times to determine their capabilities for measuring column densities and neutral fractions with the Ly-alpha damping wings of high-redshift GRBs. We find that both spectrographs will be highly effective for obtaining column density estimates. Despite the presence of telluric lines, we find that ELT HARMONI will be a powerful instrument for retrieving accurate neutral fraction estimates, but JWST NIRSpec will be vital for obtaining neutral fraction measurements for bright GRBs that fall in redshift ranges where ELT is less effective. Additionally, shorter JWST Target of Opportunity (ToO) follow-up times would greatly increase the accuracy of neutral fraction estimates obtained with NIRSpec spectra.