(Re)Solving Reionization with Ly{\alpha}: How Bright Ly{\alpha} Emitters account for the $z\approx2-8$ Cosmic Ionizing Background

The cosmic ionizing emissivity from star-forming galaxies has long been anchored to UV luminosity functions. Here we introduce an emissivity framework based on Ly$\alpha$ emitters (LAEs), which naturally hones in on the subset of galaxies responsible for the ionizing background due to the intimate connection between the production and escape of Ly$\alpha$ and LyC photons. Using constraints on the escape fractions of bright LAEs ($L_{\rm{Ly\alpha}}>0.2 L^{*}$) at $z\approx2$ obtained from resolved Ly$\alpha$ profiles, and arguing for their redshift-invariance, we show that: (i) quasars and LAEs together reproduce the relatively flat emissivity at $z\approx2-6$, which is non-trivial given the strong evolution in both the star-formation density and quasar number density at these epochs and (ii) LAEs produce late and rapid reionization between $z\approx6-9$ under plausible assumptions. Within this framework, the $>10\times$ rise in the UV population-averaged $f_{\rm{esc}}$ between $z\approx3-7$ naturally arises due to the same phenomena that drive the growing Ly$\alpha$ emitter fraction with redshift. Generally, a LAE dominated emissivity yields a peak in the distribution of the ionizing budget with UV luminosity as reported in latest simulations. Using our adopted parameters ($f_{\rm{esc}}=50\%$, $\xi_{\rm{ion}}=10^{25.9}$ Hz erg$^{-1}$ for half the bright LAEs), a highly ionizing minority of galaxies with $M_{\rm UV}<-17$ accounts for the entire ionizing budget from star-forming galaxies. Rapid flashes of LyC from such rare galaxies produce a "disco" ionizing background. We conclude proposing tests to further develop our suggested Ly$\alpha$-anchored formalism.