The spectra of several high–redshift ( z > 6 ) quasars have shown indications for a Gunn-Peterson ( GP ) damping wing , suggesting a substantial mean neutral hydrogen fraction ( \bar { x } _ { HI } ^ { IGM } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } % \raise 1.0 pt \hbox { $ > $ } } 0.03 ) in the z \approx 6 intergalactic medium ( IGM ) .
However , previous analyses assumed that the IGM was uniformly ionized outside of the quasar ’ s HII region .
Here we relax this assumption and model patchy reionization scenarios for a range of IGM and quasar parameters .
Compared to uniform reionization , patchy reionization imprints a different average damping wing profile with an associated sightline-to-sightline scatter .
We quantify the impact of these differences on the inferred \bar { x } _ { HI } ^ { IGM } , by fitting the spectra of three quasars : SDSS J1148+5251 ( z = 6.4189 ) , J1030+0524 ( z = 6.308 ) , and J1623+3112 ( z = 6.247 ) .
We find that the best-fit values of \bar { x } _ { HI } ^ { IGM } in the patchy models agree well with the uniform case .
More importantly , we confirm that the observed spectra favor the presence of a GP damping wing , with peak likelihoods decreasing by factors of \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox { $ > $ } } few – 10 when the spectra are modeled without a damping wing .
We also find that the Ly \alpha absorption spectra , by themselves , can not distinguish the damping wing in a relatively neutral IGM from a damping wing in a highly ionized IGM , caused either by an isolated neutral patch , or by a damped Ly \alpha absorber ( DLA ) .
However , neutral patches in a highly ionized universe ( \bar { x } _ { HI } ^ { IGM } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } % \raise 1.0 pt \hbox { $ < $ } } 10 ^ { -2 } ) , and DLAs with the large required column densities ( N _ { HI } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } \raise 1.0 pt \hbox% { $ > $ } } { few } \times 10 ^ { 20 } { cm ^ { -2 } } ) are both rare .
As a result , when we include reasonable prior probabilities for the line of sight ( LOS ) to intercept either a neutral patch or a DLA at the required distance of \sim 40 - 60 comoving Mpc away from the quasar , we find strong lower limits on the neutral fraction in the IGM , \bar { x } _ { HI } ^ { IGM } \mathrel { \hbox to 0.0 pt { \lower 4.0 pt \hbox { $ \sim$ } } % \raise 1.0 pt \hbox { $ > $ } } 0.1 ( at 95 % confidence ) .
This supports earlier claims that a substantial global fraction of hydrogen in the z \approx 6 IGM is in neutral form .