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 greater than or similar to10(4) K) metal-free protogalaxies is studied. In particular, we focus on the effect of H-2 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 (similar to10(3) M-circle dot), 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 similar to10 M-circle dot to subsolar scales. In compact clouds (less than or similar to1.6 kpc for clouds of gas mass 10(8) M-circle dot), 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-circle dot and a few x 10 M-circle dot. The high-mass portion of the IMF, xi(high) (m(*)), is found to be a very steep function of the stellar mass m(*), xi(high) (m(*)) proportional to 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.