An upper limit on the mass of a primordial star due to the formation of an HII region: the effect of ionizing radiation force

We investigate analytically the formation of an H II region in the accreting envelope of a newborn star. Special care is taken to examine the role of ionizing radiation force. This effect modifies velocity and density distributions, and thereby affects the expansion of the H II region. As a result, the upper limit of the stellar mass imposed by the growth of an H II region around a forming star is increased by a larger factor than the previous estimate. In particular, for a star forming out of metal-free gas, this mechanism does not impose a firm upper limit on its mass.