The Minimum Mass of the First Stars and the Anthropic Principle

It was recently shown that the initial mass function (IMF) in the Galactic disk increases monotonically with decreasing mass and is reasonably well described by a power law n(m) ∝ m−αdisk with αdisk ∼ 2±0.5 from ∼ 0.6M⊙ down to the hydrogenburning limit 1). The bimodal IMF with a turn-over around ∼ 0.2M⊙ 2) is shown to be due to unresolved binaries in the photometric luminosity function. In the Galactic disk, grains made from heavy metals are the main coolants in the star formation process. While in the formation of the first stars after the recombination of the universe, hydrogen molecules are the only coolants for temperature below 2000K since in the Big Bang Nucleosynthesis no nuclei heavier than B8 are formed. This implies that the star formation process of the first stars may be different from the present one. For example, the power index of the IMF of the first stars αfirst may be completely different from αdisk. The lower end of the mass of the stars in the present IMF is not known either. One might think that the lower end should be ∼ 0.08M⊙ because this is the lower limit of the hydrogen-burning star. However in the Hayashi phase, the pre-main sequence star itself does not know if the hydrogen is ignited in the end. At present there is no reason to believe that only stars of mass larger than ∼ 0.08M⊙ are formed. In reality the existence of brown dwarfs (=low mass stars of mass less than ∼ 0.08M⊙ ) has been confirmed observationally 3) and microlensing events opened the possibility that the halo of our Galaxy might consist of such dim brown dwarfs 4).