Quasar Str\"omgren Spheres Before Cosmological Reionization

Ionizing sources embedded in the neutral intergalactic medium (IGM) before cosmological reionization generate discrete HII regions. We show that a sufficiently bright quasar (for example, one tenth as luminous as that recently discovered by Fan et al.) can ionize a large volume, allowing the transmission of a substantial fraction of the flux of its intrinsic Lyman alpha emission line on both sides of the Lyman alpha wavelength. The observed line profile is richly informative. We show that a sufficiently accurate, high spectral resolution ($R\approx 10^4$) measurement of the line profile of a bright quasar is feasible using the Next Generation Space Telescope (NGST) as well as large ground-based telescopes. Such a measurement has two potentially important applications. First, the red side of the Lyman alpha emission line provides a way to measure the quasar lifetime. Second, the blue side provides a direct measure of the density fluctuations of the intergalactic medium at the quasar redshift. The estimate of the absorption of the red side is limited by the accuracy to which the intrinsic profile of the Lyman alpha emission line is known. The blue side, however, does not sensitively depend on the intrinsic profile, because the former is much narrower than the latter.