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tokens: by the FWHM. Given the nearly symmetric double-peaked profile of A370p_z1 and the small peak separation, we restrict our analysis to relatively small N H i and v exp values because it is well known that high column densities and shell velocities would significantly broaden the line and erase the blue peak, respectively (Verhamme, Schaerer Maselli 2006 ). We perform a quantitative comparison between the observed line profile and the models using the χ 2 statistic. We find that models minimizing the reduced χ 2 preferentially select low N H i (), static geometries ( v exp = 0), low dust content, small b values ( b = 20) and relatively broad input lines (). We show the best-fitting model in Fig. 4 which corresponds to the following parameter set: . We can derive the LyC escape fraction from the best-fitting column density = 99 per cent, where σ 912 = 6.35 × 10 −18 is the H i photoionization cross-section at the Lyman limit. While several models could match the positions of peak emission within the errors, the model is the only one to reproduce the shallow central depression of the profile which is the important signature of a low H i opacity (Fig. 4 ). Searching a finer parameter grid is beyond the scope of this paper, but we note that even when adopting a higher column density cm −2 , the escape fraction remains very high (94 per cent). Figure 4. Comparison of RASCAS models, smoothed by the resolution of X-Shooter, of Lyman α transfer through non-expanding shells of homogeneous gas with the observed Lyman α profile. The best-fitting model (blue) has which correspond to a high LyC escape fractions . We also show examples of models with (dashed orange, dash–dotted green), which would imply . 3.2 Did A370p_z1 self-ionize its local H <sc>ii</sc> bubble? The detection of the blue peak in the Lyman α indicates A370p_z1 sits in a large ionized bubble, otherwise the damping wing of even a partially neutral IGM would have absorbed it. Given its high escape fraction, we now consider whether A370p_z1 could have self-ionized its local H ii bubble. The blue wing extends to λ = 9479.2 Å, from the line centre, corresponding to a physical distance r H ii > 0.26 ± 0.04 pMpc. This estimate neglects any velocity offset between the Lyman α absorption dip from which we have derived the redshift and the systemic redshift as defined by more reliable tracers such as nebular absorption lines. These velocities are however found to be (Gazagnes et al. 2020 ), which, in the worst case, would therefore require a larger ionized bubble for the blue wing to be transmitted (≲ 0.5 pMpc). We also neglect peculiar velocities of the galaxy with respect to the ionized bubble gas which would redshift(blueshift) the Lyman α photons and decrease(increase) the bubble size needed for the blue wing to escape. We now estimate the volume that could have been reionized by A370p_z1 by redshift z = 6.803 and whether its radiation is sufficient to reduce the opacity of the surrounding gas to