We describe how star formation is expected to proceed in the early metal-free
Universe, focusing on the very first generations of stars. We then discuss how
the star formation process may change as the effects of metallicity, external
radiative feedback, and magnetic and turbulent support of the gas become more
important. The very first stars (Pop III.1) have relatively simple initial
conditions set by cosmology and the cooling properties of primordial gas. We
describe the evolution of these stars as they grow in mass by accretion from
their surrounding gas cores and how the accretion process is affected and
eventually terminated by radiative feedback processes, especially HII region
expansion and disk photoevaporation. The ability of the protostar and its disk
to generate dynamically important magnetic fields is reviewed and their effects
discussed. Pop III.1 star formation is likely to produce massive (~100-200Msun)
stars that then influence their surroundings via ionization, stellar winds, and
supernovae. These processes heat, ionize and metal-enrich the gas, thus
altering the initial conditions for the next generation of star formation.
Stars formed from gas that has been altered significantly by radiative and/or
mechanical feedback, but not by metal enrichment (Pop III.2) are expected to
have significantly smaller masses than Pop III.1 stars because of more
efficient cooling from enhanced HD production. Stars formed from gas that is
metal-enriched to levels that affect the dynamics of the collapse (the first
Pop II stars) are also expected to have relatively low masses. We briefly
compare the above star formation scenarios to what is known about present-day
star formation.Comment: 16 pages, including 11 figures, Review paper to appear in "First
Stars III", eds. B. O'Shea, A. Heger and T. Abe