Two Modes of LyC Escape From Bursty Star Formation: Implications for [C II] Deficits and the Sources of Reionization

We use the SPHINX${}^{20}$ cosmological radiation hydrodynamics simulation to study how Lyman Continuum (LyC) photons escape from galaxies and the observational signatures of this escape. We define two classes of LyC leaker: Bursty Leakers and Remnant Leakers, based on their star formation rates (SFRs) that are averaged over 10 Myr (SFR${}_{10}$) or 100 Myr (SFR${}_{100}$). Both have $f_{\mathrm{e}\mathrm{s}\mathrm{c}}>20\mathrm{\%}$ and experienced an extreme burst of star formation, but Bursty Leakers have $\mathrm{S}\mathrm{F}{\mathrm{R}}_{10}>\mathrm{S}\mathrm{F}{\mathrm{R}}_{100}$, while Remnant Leakers have $\mathrm{S}\mathrm{F}{\mathrm{R}}_{10}<\mathrm{S}\mathrm{F}{\mathrm{R}}_{100}$. The maximum SFRs in these bursts were typically $\sim 100$ times greater than the SFR of the galaxy prior to the burst, a rare $2\sigma$ outlier among the general high-redshift galaxy population. Bursty Leakers are qualitatively similar to ionization-bounded nebulae with holes, exhibiting high ionization parameters and typical HII region gas densities. Remnant Leakers show properties of density-bounded nebulae, having normal ionization parameters but much lower HII region densities. Both types of leaker exhibit [CII]${}_{158\mu \mathrm{m}}$ deficits on the [CII]-SFR${}_{100}$ relation, while only Bursty Leakers show deficits when SFR${}_{10}$ is used. We predict that [CII] luminosity and SFR indicators such as H$\alpha$ and M${}_{1500\mathring{\mathrm{A}}}$ can be combined to identify both types of LyC leaker and the mode by which photons are escaping. These predictions can be tested with [CII] observations of known $z=3-4$ LyC leakers. Finally, we show that leakers with $f_{\mathrm{e}\mathrm{s}\mathrm{c}}>20\mathrm{\%}$ dominate the ionizing photon budget at $z\gtrsim 7.5$ but the contribution from galaxies with $f_{\mathrm{e}\mathrm{s}\mathrm{c}}<5\mathrm{\%}$ becomes significant at the tail-end of reionization.