The Far-Ultraviolet Continuum Slope as a Lyman Continuum Escape Estimator at High-redshift

Most of the hydrogen in the intergalactic medium (IGM) was rapidly ionized at high-redshifts. While observations have established that reionization occurred, observational constraints on the emissivity of ionizing photons at high-redshift remains elusive. Here, we present a new analysis of the Low-redshift Lyman Continuum Survey (LzLCS) and archival observations, a combined sample of 89 star-forming galaxies at z~0.3 with Hubble Space Telescope observations of their ionizing continua (or Lyman Continuum, LyC). We find a strong (6$\sigma$ significant) inverse correlation between the continuum slope at 1550\r{A} (defined as F$_\lambda\propto\lambda^{\beta}$) and both the LyC escape fraction (f$_{esc}$) and f$_{esc}$ times the ionizing photon production efficiency ($\xi_{ ion}$). On average, galaxies with redder continuum slopes have smaller f$_{esc}$ than galaxies with bluer slopes due to higher dust attenuation. More than 5% (20%) of the LyC emission escapes galaxies with $\beta$<-2.1 (-2.6). We find strong correlations between $\beta$ and the gas-phase ionization ([OIII]/[OII] flux ratio; at 7.5$\sigma$ significance), galaxy stellar mass (at 5.9$\sigma$), the gas-phase metallicity (at 4.6$\sigma$), and the observed FUV absolute magnitude (M$_{UV}$ at 3.4$\sigma$). Using previous observations of $\beta$ at high-redshift, we estimate the evolution of f$_{esc}$ with both $z$ and M$_{UV}$. The LzLCS suggest that fainter and lower mass galaxies dominate the ionizing photon budget at higher redshift, possibly due to their rapidly evolving metal and dust content. Finally, we use our correlation between $\beta$ and f$_{ esc}\times\xi_{ion}$ to predict the ionizing emissivity of galaxies during the epoch of reionization. Our estimated emissivities match IGM observations, and suggest that star-forming galaxies emit sufficient LyC photons into the IGM to exceed recombinations near redshifts of 7-8.