Determining the redshift of reionization from the spectra of high-redshift sources

The redshift at which the universe was reionized is currently unknown. We examine the optimal strategy for extracting this redshift, z(reion), from the spectra of early sources. For a source located at a redshift z(s) beyond but close to the reionization redshift, (1 + z(reion)) < (1 + z(s)) < 32/27(1 + z(reion)), the Gunn-Peterson trough splits into disjoint Ly alpha, Ly beta, and possibly higher Lyman series troughs, with some transmitted flux between these troughs. We show that although the transmitted flux is suppressed considerably by the dense Ly alpha forest at high redshifts, it could still be detectable as long as z(reion) less than or similar to 8. If the ionizing sources are bright and have a short duty cycle (e.g., if they are miniquasars or starbursts with a lifetime less than or similar to 10(6) yr), then breakthrough occurs shortly after the H II regions around them overlap, and the transmitted flux provides a measurement of z(reion). The Next Generation Space Telescope will reach the spectroscopic sensitivity required for such a measurement.