We report the results of a study of the rest-frame UV spectrum of the Cosmic Eye, a luminous Lyman break galaxy at z=3.07331 gravitationally lensed by a factor of 25. The spectrum, recorded with the ESI spectrograph on the Keck II telescope, is rich in absorption features from the gas and massive stars in this galaxy. The interstellar absorption lines are resolved into two components of approximately equal strength and each spanning several hundred km/s in velocity. One component has a net blueshift of -70 km/s relative to the stars and H II regions and presumably arises in a galaxy-scale outflow similar to those seen in most star-forming galaxies at z = 2-3. The other is more unusual in showing a mean redshift of +350 km/s relative to the systemic redshift; possible interpretations include a merging clump, or material ejected by a previous star formation episode and now falling back onto the galaxy, or more simply a chance alignment with a foreground galaxy. In the metal absorption lines, both components only partially cover the OB stars against which they are being viewed. We tentatively associate the redshifted component with the strong damped Lyman alpha line, indicative of a column density N(H I) = (3.0 +/- 0.8) x 10(21) atoms/cm2, and propose that it provides the dust `foreground screen responsible for the low ratio of far-infrared to UV luminosities of the Cosmic Eye. Compared to other well-studied examples of strongly lensed galaxies, we find that the young stellar population of the Cosmic Eye is essentially indistinguishable from those of the Cosmic Horseshoe and MS 1512-cB58, while the interstellar spectra of all three galaxies are markedly different, attesting to the real complexity of the interplay between starbursts and ambient interstellar matter in young galaxies (abridged).
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