Arguably the best hope of understanding the tail end of the reionization process at redshift z>6 is through the detection and characterization of the Gunn-Peterson (GP) damping wing absorption in bright quasar spectra. Unlike the direct use of the GP trough, which probes low mean neutral hydrogen fractions of x_HI ~< 10^-3, or the use of Lyman alpha emitting galaxies or Cosmic Microwave Background (CMB) anisotropies, which probe only the range x_HI >~ 0.3, the GP damping wings can reveal large patches of gas in the intergalactic medium (IGM) where the neutral fraction is a few percent. However, the use of quasar spectra to measure GP damping wing absorption requires the modeling of the quasar's intrinsic Lyman alpha emission line. I will describe the results of a project designed to (i) use high-resolution HST spectra of the emission lines of relatively unobscured low-redshift quasars to characterize the asymmetry and variance in the shape of these lines, and (ii) compute the corresponding uncertainties in reionization constraints that will be available from a sample of z>6 quasar spectra.
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