The usefulness of H I Lyman-alpha photons for characterizing star formation in the distant universe is limited by our understanding of the astrophysical processes that regulate their escape from galaxies. These processes can only be observed in detail out to a few x100 Mpc. Past nearby (z<0.3) spectroscopic studies are based on small samples and/or kinematically unresolved data. Taking advantage of the high sensitivity of HSTs COS, we observed the Lyman-alpha lines of 20 H-alpha-selected galaxies located at <z>=0.03. The galaxies cover a broad range of luminosity, oxygen abundance, and reddening. In this paper, we characterize the observed Lyman-alpha lines and establish correlations with fundamental galaxy properties. We find seven emitters. These host young (le 10 Myr) stellar populations, have rest-frame equivalent widths in the range 1-12 AA, and have Lyman-alpha escape fractions within the COS aperture in the range 1-12 %. One emitter has a double-peaked Lyman-alpha with peaks 370 km/s apart and a stronger blue peak. Excluding this object, the emitters have Lyman-alpha and O I lambda 1302 offsets from H-alpha in agreement with expanding shell models and LBG observations. The absorbers have offsets that are almost consistent with a static medium. We find no one-to-one correspondence between Lyman-alpha emission and age, metallicity, or reddening. Thus, we confirm that Lyman-alpha is enhanced by outflows and is regulated by the dust and H I column density surrounding the hot stars.
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