We compare the physical and morphological properties of z ~ 2 Lyman-alpha emitting galaxies (LAEs) identified in the HETDEX Pilot Survey and narrow band studies with those of z ~ 2 optical emission line galaxies (oELGs) identified via HST WFC3 infrared grism spectroscopy. Both sets of galaxies extend over the same range in stellar mass (7.5 < logM < 10.5), size (0.5 < R < 3.0 kpc), and star-formation rate (~1 < SFR < 100). Remarkably, a comparison of the most commonly used physical and morphological parameters -- stellar mass, half-light radius, UV slope, star formation rate, ellipticity, nearest neighbor distance, star formation surface density, specific star formation rate, [O III] luminosity, and [O III] equivalent width -- reveals no statistically significant differences between the populations. This suggests that the processes and conditions which regulate the escape of Ly-alpha from a z ~ 2 star-forming galaxy do not depend on these quantities. In particular, the lack of dependence on the UV slope suggests that Ly-alpha emission is not being significantly modulated by diffuse dust in the interstellar medium. We develop a simple model of Ly-alpha emission that connects LAEs to all high-redshift star forming galaxies where the escape of Ly-alpha depends on the sightline through the galaxy. Using this model, we find that mean solid angle for Ly-alpha escape is 2.4+/-0.8 steradians; this value is consistent with those calculated from other studies.
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