We perform joint modeling of the composite rest-frame far-UV (FUV) and optical spectra of redshift 1.85<z<3.49 star-forming galaxies to deduce key properties of the massive stars, ionized ISM, and neutral ISM, with the aim of investigating the principal factors affecting the production and escape of Ly-alpha (Lya) photons. Our sample consists of 136 galaxies with deep Keck/LRIS and MOSFIRE spectra covering, respectively, Ly-beta through CIII] 1907, 1909; and [OII], [NeIII], H-beta, [OIII], H-alpha, [NII], and [SII]. Spectral and photoionization modeling indicate that the galaxies are uniformly consistent with stellar population synthesis models that include the effects of stellar binarity. Over the dynamic range of our sample, there is little variation in stellar and nebular abundance with Lya equivalent width, W(Lya), and only a marginal anti-correlation between age and W(Lya). The inferred range of ionizing spectral shapes is insufficient to solely account for the variation in W(Lya). Rather, the covering fraction of optically-thick HI appears to be the principal factor modulating the escape of Lya, with most of the Lya photons in down-the-barrel observations of galaxies escaping through low-column-density or ionized channels in the ISM. Our analysis shows that a high star-formation-rate surface density, Sigma_SFR, particularly when coupled with a low galaxy potential (i.e., low stellar mass), can aid in reducing the covering fraction and ease the escape of Lya photons. We conclude with a discussion of the implications of our results for the escape of ionizing radiation at high redshift.
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