The Physics of Indirect Estimators of Lyman Continuum Escape and their Application to High-Redshift JWST Galaxies

Reliable indirect diagnostics of LyC photon escape from galaxies are required to understand which sources were the dominant contributors to reionization. While multiple LyC escape fraction ($f_{\rm esc}$) indicators have been proposed to trace favourable conditions for LyC leakage from the interstellar medium of low-redshift ''analog'' galaxies, it remains unclear whether these are applicable at high redshifts where LyC emission cannot be directly observed. Using a library of 14,120 mock spectra of star-forming galaxies with redshifts $4.64 \leq z \leq 10$ from the SPHINX$^{20}$ cosmological radiation hydrodynamics simulation, we develop a framework for the physics that leads to high $f_{\rm esc}$. We investigate LyC leakage from our galaxies based on the criteria that successful LyC escape diagnostics must i) track a high specific star formation rate, ii) be sensitive to stellar population age in the range $3.5-10~$Myr representing the times when supernova first explode to when LyC production significantly drops, and iii) include a proxy for neutral gas content and gas density in the interstellar medium. ${\rm O}_{32}$, $\Sigma_{\rm SFR}$, M$_{\rm UV}$, and H$\beta$ equivalent width select for one or fewer of our criteria, rendering them either necessary but insufficient or generally poor diagnostics. In contrast, UV slope ($\beta$), and ${\rm E(B-V)}$ match two or more of our criteria, rendering them good $f_{\rm esc}$ diagnostics (albeit with significant scatter). Using our library, we build a quantitative model for predicting $f_{\rm esc}$ based on direct observables. When applied to bright $z > 6$ Ly$\alpha$ emitters observed with JWST, we find that the majority of them have $f_{\rm esc} \lesssim 10\%$.