We analyze the spectra of $10$ Green Pea galaxies, previously studied by Henry et al. (2015), using a semi-analytical line transfer (SALT) model to interpret emission and absorption features observed in UV galactic spectra. We focus our analysis on various ionization states of silicon, associated with the cool ($sim 10^4$ K) and warm ($sim 10^5$ K) gas. By analyzing low-ionization lines, we study the relationships between the distribution and kinematics of the outflowing H I gas and the observed Ly$alpha$ escape fraction, $f_{esc}^{Lyalpha}$, as well as the Ly$alpha$ emission peak separation, $Delta_{peak}$. We find that outflow geometries which leave a portion of the source uncovered along the line of sight create the best conditions for Ly$alpha$ escape and have narrow peak separations, while geometries which block the observers view of the source create the worst conditions for Ly$alpha$ escape and have large peak separations. To isolate the effects of outflow kinematics, we restricted our testing set to galaxies with spherical outflows and found that $f_{esc}^{Lyalpha}$ and the Ly$alpha$ luminosity both increase with the extent of the galactic winds. A simple estimate suggests that the collisional excitation of neutral hydrogen by free electrons in the cool gas of the winds can account for the Ly$alpha$ luminosity observed in these objects. Finally, we speculate on the relationship between outflows and the escape of ionizing radiation from the CGM.
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