A unique window into the Epoch of Reionisation: A double-peaked Lyman-$\alpha$ emitter in the proximity zone of a quasar at $z\sim 6.6$

We present a study of a double-peaked Ly$\alpha$ emitter, named LAE-11, found in the proximity zone of QSO J0910-0414 at $z\sim 6.6$. We use a combination of deep photometric data from Subaru Telescope, HST, and JWST with spectroscopic data from Keck/DEIMOS, NIRCam WFSS and NIRSpec MSA to characterise the ionising and general properties of the galaxy, as well as the quasar environment surrounding it. We detect Ly$\alpha$, H$\beta$, [OIII] doublet, and H$\alpha$ emission lines in the various spectral datasets. The presence of a double-peaked Ly$\alpha$ line in the spectrum allows us to characterise the opening angle and lifetime of the QSO as ${\theta }_Q>49.62$° and $t_Q>3.8\times {10}^5$ years. LAE-11 is a fairly bright (M${}_{\mathrm{U}\mathrm{V}}=-19.84_{-0.16}^{+0.14}$), blue galaxy with a UV slope of $\beta =-2.61_{-0.08}^{+0.06}$. Since the galaxy is located in a quasar-ionised region, we have a unique opportunity to measure the escape fraction of Lyman Continuum photons using the un-attenuated double-peaked Ly$\alpha$ emission profile and its equivalent width at such high redshift. We employ diagnostics which do not rely on the detection of Ly$\alpha$ for comparison, and find that all tracers of ionising photon leakage agree within 1$\sigma$ uncertainty. We measure a moderate escape of Lyman Continuum photons from LAE-11 of $f_{\mathrm{e}\mathrm{s}\mathrm{c}}^{\mathrm{L}\mathrm{y}\mathrm{C}}=(8-33)\mathrm{\%}$. Detections of both H$\alpha$ and H$\beta$ emission lines allow for separate measurements of the ionising photon production efficiency, resulting with $\log ({\xi }_{\mathrm{i}\mathrm{o}\mathrm{n}}\mathrm{/}\mathrm{H}\mathrm{z}\mathrm{e}\mathrm{r}{\mathrm{g}}^{-1})=25.59\pm 0.08$ and $25.65\pm 0.09$, for H$\alpha$ and H$\beta$, respectively. The total ionising output of LAE-11, $\log (f_{\mathrm{e}\mathrm{s}\mathrm{c}}^{\mathrm{L}\mathrm{y}\mathrm{C}}{\xi }_{\mathrm{i}\mathrm{o}\mathrm{n},\mathrm{H}\alpha }\mathrm{/}\mathrm{H}\mathrm{z}\mathrm{e}\mathrm{r}{\mathrm{g}}^{-1})=24.85_{-0.34}^{+0.24}$, is higher than the value of $24.3-24.8$ which is traditionally assumed as needed to drive Reionisation forward.