We investigate the formation by accretion of massive primordial protostars in the range 10 to 300 M_⊙. The high accretion rate used in the models (M = 4. 4 x 10 ~(-3) M_⊙ yr ~(-1)) causes the structure and evolution to differ significantly from those of both present-day protostars and prim-ordial zero-age main sequence stars. The stellar surface is not visible throughout most of the main accretion phase, since a photosphere is formed in the infalling envelope. Significant nuclear burning does not take place until a protostellar mass of about 80 M_⊙. As the interior luminosity approaches the Eddington luminosity, the protostellar radius rapidly expands owing to the radiation pressure. Eventually, a final swelling occurs when the stellar mass reaches about 300 M_⊙. This expansion is likely to signal the end of the main accretion phase, thus setting an upper limit to the protostellar mass formed in these conditions.
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