Ly{\alpha} profile shape as an escape-fraction diagnostic at high redshift

While the shape of the Ly$\alpha$ profile is viewed as one of the best tracers of ionizing-photon escape fraction ($f_{esc}$) within low redshift (z~0.3) surveys of the Lyman continuum, this connection remains untested at high redshift. Here, we combine deep, rest-UV Keck/LRIS spectra of 80 objects from the Keck Lyman Continuum Spectroscopic Survey with rest-optical Keck/MOSFIRE spectroscopy in order to examine potential correlations between Ly$\alpha$ profile shape and the escape of ionizing radiation within z~3 star-forming galaxies. We measure the velocity separation between double-peaked Ly$\alpha$ emission structure (v$_{\rm sep}$), between red-side Ly$\alpha$ emission peaks and systemic (v$_{\rm Ly\alpha,red}$), and between red-side emission peaks and low-ionization interstellar absorption lines (v$_{\rm Ly\alpha-LIS}$). We find that the IGM-corrected ratio of ionizing to non-ionizing flux density is significantly higher in KLCS objects with lower v$_{\rm Ly\alpha,red}$. We find no significant trend between measures of ionizing-photon escape and v$_{\rm Ly\alpha-LIS}$. We compare our results to measurements of z~0.3 "Green Peas" from the literature and find that KLCS objects have larger v$_{\rm sep}$ at fixed v$_{\rm Ly\alpha,red}$, larger $f_{esc}$ at fixed v$_{\rm Ly\alpha,red}$, and higher v$_{\rm Ly\alpha,red}$ overall than z~0.3 analogs. We conclude that the Ly$\alpha$ profile shapes of our high-redshift sources are fundamentally different, and that measurements of profile shape such as v$_{\rm Ly\alpha,red}$ map on to $f_{esc}$ in different ways. We caution against building reionization-era $f_{esc}$ diagnostics based purely on Ly$\alpha$ profiles of low-redshift dwarf galaxies. Tracing v$_{\rm sep}$, v$_{\rm Ly\alpha,red}$, and $f_{esc}$ in a larger sample of z~3 galaxies will reveal how these variables may be connected for galaxies at the epoch of reionization.