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We describe a technique that for the first time measures star formation rates(SFRs) in damped Lyman alpha systems(DLAs) directly. We assume that massivestars form in DLAs, and that the FUV radiation they emit heats the gas by thegrain photoelectric mechanism. We infer the heating rate from the cooling ratemeasured by the strength of CII* 1335.7 absorption. Since the heating rate isproportional to the dust-to-gas ratio and the SFR per unit area, we deduce theSFR per unit area for DLAs in which both quantities have been measured. Weconsider models in which the the dust comprises carbonaceous or silicategrains. We present two-phase models where the cold neutral medium (CNM) andwarm neutral medium (WNM) are in pressuer equilibrium. In the CNM model the thesightline goes throught the CNM and WNM, while in the WNM model it goes onlythrough the WNM. Since the grain photoelectric heating efficiency is at least10 times higher in the CNM than in the WNM, CII* absorption mainly arises inthe CNM in the CNM model. But in the WNM model all of the CII* absorptionarises in the WNM. We use CII* absorption lines to derive the SFR per unit areafor a sample of ~ 30 DLAs in which the dust-to-gas ratio has been inferred fromelement depletion patterns. We show that the resulting SFR per unit areacorresponds to an average over the star forming volume of galaxy hosting theDLA rather than to local star formation along the line of sight. We find theaverage SFR per unit area and equals10$^{-2.2}$ M$_{\odot}$yr$^{-1}$kpc$^{-2}$for the CNM model and 10$^{-1.3}$ M$_{\odot}$yr$^{-1}$kpc$^{-2}$ for the WNMmodel. The SFR per unit area in the CNM solution is similar to that measured inthe Milky Way ISM.Comment: To Appear in the Astrophysical Journa

Cii* Absorption in Damped Lyα Systems. I. Star Formation Rates in a Two‐Phase Medium