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Constraining the escape fraction of Lyman Continuum (LyC) photons fromhigh-redshift galaxies is crucial to understanding reionization. Recentobservations have demonstrated that various characteristics of the Ly$\alpha$emission line correlate with the inferred LyC escape fraction ($f_{\rmesc}^{\rm LyC}$) of low-redshift galaxies. Using a data-set of 9,600 mockLy$\alpha$ spectra of star-forming galaxies at $4.64 \leq z \leq 6$ from theSPHINX$^{20}$ cosmological radiation hydrodynamical simulation, we study theescape of Ly$\alpha$ and LyC photons. We find that our mock Ly$\alpha$observations are representative of high-redshift observations and that typicalobservational methods tend to over-predict the Ly$\alpha$ escape fraction($f_{\rm esc}^{\rm Ly\alpha}$) by as much as two dex. We investigate thecorrelations between $f_{\rm esc}^{\rm LyC}$ and $f_{\rm esc}^{\rm Ly\alpha}$,Ly$\alpha$ equivalent width ($W_{\lambda}({\rm Ly\alpha})$), peak separation($v_{\rm sep}$), central escape fraction ($f_{\rm cen}$), and red peakasymmetry ($A_f^{\rm red}$). We find that $f_{\rm esc}^{\rm Ly\alpha}$ and$f_{\rm cen}$ are good diagnostics for LyC leakage, selecting for galaxies withlower neutral gas densities and less UV attenuation that have recentlyexperienced supernova feedback. In contrast, $W_{\lambda}({\rm Ly\alpha})$ and$v_{\rm sep}$ are found to be necessary but insufficient diagnostics, while$A_f^{\rm red}$ carries little information. Finally, we use stacks ofLy$\alpha$, H$\alpha$, and F150W mock surface brightness profiles to find thatgalaxies with high $f_{\rm esc}^{\rm LyC}$ have less extended Ly$\alpha$ andF150W but larger H$\alpha$ haloes than their non-leaking counterparts. Thisconfirms that Ly$\alpha$ spectral profiles and surface brightness morphologycan be used to better understand the escape of LyC photons from galaxies duringthe Epoch of Reionization.

The Great Escape: Understanding the Connection Between Ly$\alpha$ Emission and LyC Escape in Simulated JWST Analogues