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Arguably the best hope of understanding the tail end of the re‐ionization of the intergalactic medium (IGM) at redshift   z  &gt; 6  is through the detection and characterization of the Gunn–Peterson damping wing absorption of the IGM in bright quasar spectra. However, the use of quasar spectra to measure the IGM damping wing requires a model of the quasar's intrinsic Lyman α emission line. Here we quantify the uncertainties in the intrinsic line shapes, and how those uncertainties affect the determination of the IGM neutral fraction. We have assembled a catalogue of high‐resolution  Hubble Space Telescope  spectra of the emission lines of unobscured low‐redshift quasars, and have characterized the variance in the shapes of their lines. We then add simulated absorption from the high‐redshift IGM to these quasar spectra in order to determine the corresponding uncertainties in re‐ionization constraints using current and future samples of   z  &gt; 6  quasar spectra. We find that, if the redshift of the Lyman α emission line is presumed to coincide with the systemic redshift determined from metal lines, the inferred IGM neutral fraction is systematically biased to low values due to a systematic blueshift of the Lyman α line relative to the metal lines. If a similar blueshift persists in quasars at   z  &gt; 6 , this bias strengthens previous claims of a significant neutral hydrogen fraction at   z ≈ 6 . The bias can be reduced by including a Lyman α blueshift in the modelling procedure, or by excising wavelengths near the Lyman α line centre from the modelling. Intrinsic Lyman α line shape variations still induce significant scatter in the inferred  x  IGM  values. Nevertheless, this scatter still allows a robust distinction between a highly ionized  ( x  IGM ∼ 10 −3 )  and a neutral  ( x  IGM = 1)  IGM with even a few bright quasars. We conclude that if the variations of the intrinsic Lyman α emission line shapes in high‐ z  quasars are similar to those at low‐ z , this variation will not limit the usefulness of quasar spectra in probing re‐ionization.

Probing re‐ionization with quasar spectra: the impact of the intrinsic Lyman α emission line shape uncertainty