The mass spectrum of metal-free stars resulting from photodissociation feedback: A scenario for the formation of low-mass population III stars

The initial mass function (IMF) of metal-free stars that form in the initial starburst of massive (virial temperatures ≳ 10⁴ K) metal-free protogalaxies is studied. In particular, we focus on the effect of H₂ photo-dissociation by preexisting stars on the fragmentation mass scale, presumedly determined by the Jeans mass at the end of the initial free-fall phase, i.e., at the so-called loitering phase, characterized by the temporary temperature minimum. Photodissociation diminishes the Jeans mass at the loitering phase, thereby reducing the fragmentation mass scale of primordial clouds. Thus, in a given cloud, far-ultraviolet (FUV) radiation from the first star, which is supposedly very massive (∼10³ M⊙), reduces the mass scale for subsequent fragmentation. Through a series of similar processes the IMF for metal-free stars is established. If FUV radiation exceeds a threshold level, the star-forming clumps collapse solely through atomic cooling. Correspondingly, the fragmentation scale drops discontinuously from a few × 10 M⊙ to subsolar scales. In compact clouds (≲, 1. 6 kpc for clouds of gas mass 10⁸ M⊙), this level of radiation field is attained and subsolar-mass stars are formed, even in a metal-free environment. Consequently, the IMF becomes bimodal, with peaks at a few tenths M⊙ and a few × 10 M⊙. The high-mass portion of the IMF, ξ_high(m*), is found to be a very steep function of the stellar mass m*, ξ_high (m*) ∝ m* ^-5 Therefore, the typical mass scale of metal-free stars is significantly smaller than that of the very first stars. In an appendix we study the thermal instability in collapsing primordial prestellar cores and discuss why the thermal instability occurring during the three-body H ₂ formation does not appear to manifest itself in causing further fragmentation of such cores.