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The spectra of several high-redshift (z>6) quasars have shown evidence for aGunn-Peterson (GP) damping wing, indicating a substantial mean neutral hydrogenfraction (x_HI > 0.03) in the z ~ 6 intergalactic medium (IGM). However,previous analyses assumed that the IGM was uniformly ionized outside of thequasar's HII region. Here we relax this assumption and model patchyreionization scenarios for a range of IGM and quasar parameters. We quantifythe impact of these differences on the inferred x_HI, by fitting the spectra ofthree quasars: SDSS J1148+5251 (z=6.419), J1030+0524 (z=6.308), and J1623+3112(z=6.247). We find that the best-fit values of x_HI in the patchy models agreewell with the uniform case. More importantly, we confirm that the observedspectra favor the presence of a GP damping wing, with peak likelihoodsdecreasing by factors of > few - 10 when the spectra are modeled without adamping wing. We also find that the Ly alpha absorption spectra, by themselves,cannot distinguish the damping wing in a relatively neutral IGM from a dampingwing in a highly ionized IGM, caused either by an isolated neutral patch, or bya damped Ly alpha absorber (DLA). However, neutral patches in a highly ionizeduniverse (x_HI < 0.01), and DLAs with the large required column densities (N_HI> few x 10^{20} cm^{-2}) are both rare. As a result, when we include reasonableprior probabilities for the line of sight (LOS) to intercept either a neutralpatch or a DLA at the required distance of ~ 40-60 comoving Mpc away from thequasar, we find strong lower limits on the neutral fraction in the IGM, x_HI >0.1 (at 95% confidence). This strengthens earlier claims that a substantialglobal fraction of hydrogen in the z~6 IGM is in neutral form.

Evidence of Gunn-Peterson damping wings in high-z quasar spectra: strengthening the case for incomplete reionization