Multivariate Predictors of LyC Escape I: A Survival Analysis of the Low-redshift Lyman Continuum Survey

To understand how galaxies reionized the universe, we must determine how the escape fraction of Lyman Continuum (LyC) photons (fesc) depends on galaxy properties. Using the z~0.3 Low-redshift Lyman Continuum Survey (LzLCS), we develop and analyze new multivariate predictors of fesc. These predictions use the Cox proportional hazards model, a survival analysis technique that incorporates both detections and upper limits. Our best model predicts the LzLCS fesc detections with a root-mean-square (RMS) scatter of 0.31 dex, better than single-variable correlations. According to ranking techniques, the most important predictors of fesc are the equivalent width (EW) of Lyman-series absorption lines and the UV dust attenuation, which track line-of-sight absorption due to HI and dust. The HI absorption EW is uniquely crucial for predicting fesc for the strongest LyC emitters, which show properties similar to weaker LyC emitters and whose high fesc may therefore result from favorable orientation. In the absence of HI information, star formation rate surface density ($\Sigma_{\rm SFR}$) and [O III]/[O II] ratio are the most predictive variables and highlight the connection between feedback and fesc. We generate a model suitable for z>6, which uses only the UV slope, $\Sigma_{\rm SFR}$, and [O III]/[O II]. We find that $\Sigma_{\rm SFR}$ is more important in predicting fesc at higher stellar masses, whereas [O III]/[O II] plays a greater role at lower masses. We also analyze predictions for other parameters, such as the ionizing-to-non ionizing flux ratio and Ly=alpha escape fraction. These multivariate models represent a promising tool for predicting fesc at high redshift.