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We present a theoretical model for primordial star formation. First wedescribe the structure of the initial gas cores as virialized,quasi-hydrostatic objects in accord with recent high resolution numericalstudies. The accretion rate can then be related to characteristic densities andtemperatures that are set by the cooling properties of molecular hydrogen. Weallow for rotation of the gas core, assuming angular momentum conservationinside the sonic point of the flow. In the typical case, most mass then reachesthe star via an accretion disk. The structure of the inner region of this diskis described with the standard theory of viscous disks, but with allowance forthe substantial energies absorbed in ionizing and dissociating the gas. Thesize of the protostar and its luminosity depend upon the accretion rate, theenergetics of the accreting gas, and the ability of the radiation to escapefrom the stellar accretion shock. We combine these models for the infall rate,inner disk structure, and protostellar evolution to predict the radiation fieldthat is the basis for radiative feedback processes acting against infall (PaperII). For realistic initial angular momenta, the photosphere of the protostar ismuch smaller and hotter than in the spherical case, leading to strongerradiative feedback at earlier stages in the evolution. In particular, once thestar is older than its Kelvin-Helmholtz time, contraction towards the mainsequence causes a rapid increase in ionizing and far-ultraviolet luminosity atmasses ~30Msun in the fiducial case. Since the cores out of which the firststars formed were much more massive than 30Msun and since feedback isdynamically unimportant at lower masses, we conclude that the first starsshould have had masses >~30Msun.Comment: 20 pages, Accepted to ApJ, some re-arrangement of text for improved  clarit

The Formation of the First Stars. I. Mass Infall Rates, Accretion Disk Structure, and Protostellar Evolution