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In this paper, we present the Ly<jats:italic>\u03b1<\/jats:italic> line profiles of the Cosmic Origins Spectrograph (COS) Legacy Archive Spectroscopic SurveY, a sample rich in spectroscopic analogs of reionization-era galaxies. A large fraction of the spectra show a complex profile, consisting of a double-peaked Ly<jats:italic>\u03b1<\/jats:italic> emission profile in the bottom of a damped, Ly<jats:italic>\u03b1<\/jats:italic> absorption trough. Such profiles reveal an inhomogeneous ISM. We successfully fit the damped Ly<jats:italic>\u03b1<\/jats:italic> absorption and the Ly<jats:italic>\u03b1<\/jats:italic> emission profiles separately, but with complementary covering factors, a surprising result because this approach requires no Ly<jats:italic>\u03b1<\/jats:italic> exchange between high-<jats:italic>N<\/jats:italic>\n                  <jats:sub>H <jats:sc>i<\/jats:sc>\n                  <\/jats:sub> and low-<jats:italic>N<\/jats:italic>\n                  <jats:sub>H <jats:sc>i<\/jats:sc>\n                  <\/jats:sub> paths. The combined distribution of column densities is qualitatively similar to the bimodal distributions observed in numerical simulations. We find an inverse relation between Ly<jats:italic>\u03b1<\/jats:italic> peak separation and the [O <jats:sc>iii<\/jats:sc>]\/[O <jats:sc>ii<\/jats:sc>] flux ratio, confirming that the covering fraction of Lyman-continuum-thin sightlines increases as the Ly<jats:italic>\u03b1<\/jats:italic> peak separation decreases. We combine measurements of Ly<jats:italic>\u03b1<\/jats:italic> peak separation and Ly<jats:italic>\u03b1<\/jats:italic> red peak asymmetry in a diagnostic diagram, which identifies six Lyman-continuum leakers in the COS Legacy Archive Spectrocopy SurveY (CLASSY) sample. We find a strong correlation between the Ly<jats:italic>\u03b1<\/jats:italic> trough velocity and the outflow velocity measured from interstellar absorption lines. We argue that greater vignetting of the blueshifted Ly<jats:italic>\u03b1<\/jats:italic> peak, relative to the redshifted peak, is the source of the well-known discrepancy between shell-model parameters and directly measured outflow properties. The CLASSY sample illustrates how scattering of Ly<jats:italic>\u03b1<\/jats:italic> photons outside the spectroscopic aperture reshapes Ly<jats:italic>\u03b1<\/jats:italic> profiles because the distances to these compact starbursts span a large range.<\/jats:p>","DOI":"10.3847\/1538-4357\/aceefd","type":"journal-article","created":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T09:59:08Z","timestamp":1696499948000},"page":"39","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":30,"title":["CLASSY VII Ly\u03b1 Profiles: The Structure and Kinematics of Neutral Gas and Implications for LyC Escape in Reionization-era Analogs*"],"prefix":"10.3847","volume":"956","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3424-3230","authenticated-orcid":true,"given":"Weida","family":"Hu","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9189-7818","authenticated-orcid":true,"given":"Crystal 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