We investigate the formation by accretion of massive primordial protostars in the range 10 to 300 M _ { \odot } .
The high accretion rate used in the models ( \dot { M } = 4.4 \times 10 ^ { -3 } M _ { \sun } { yr } ^ { -1 } ) causes the structure and evolution to differ significantly from those of both present-day protostars and primordial zero-age main sequence stars .
After an initial expansion of the radius ( for M _ { \ast } \lesssim 12 M _ { \odot } ) , the protostar undergoes an extended phase of contraction ( up to M _ { \ast } \simeq 60 M _ { \odot } ) .
The stellar surface is not visible throughout most of the main accretion phase , since a photosphere is formed in the infalling envelope .
Also , significant nuclear burning does not take place until a protostellar mass of about 80 M _ { \sun } .
As the interior luminosity approaches the Eddington luminosity , the protostellar radius rapidly expands , reaching a maximum around 100 M _ { \odot } .
Changes in the ionization of the surface layers induce a secondary phase of contraction , followed by a final swelling due to radiation pressure when the stellar mass reaches about 300 M _ { \sun } .
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 .