On Population III Star Formation

Extract

If primordial fluctuations were isothermal their amplitude at recombination would be non-linear on scales M_o ≃ 10^6÷9 M_⊙. Since the Jeans mass after recombination is M_Jo ≃ 8 × 10⁵ Ω^−1/2 M_⊙ the clouds of mass M_o would be able to form the first generation of compact objects, the so-called Population III. These clouds would acquire angular momentum via tidal interactions with their neighbours. The importance of rotation can be conveniently characterised by the spin parameter λ = V_rotation/V_free-fall and tidal interactions lead to a spin λ_o = 0.07 ± 0.03. As the cloud collapses λ increases as r^−1/2. Any fragment forming in a rotating cloud would have the same spin λ as the whole cloud. It could therefore collapse only by ≃ λ_o² in radius before centrifugal forces intervened, thus leaving a large geometrical cross-section for coalescence to be important. At radii r ≲ λ_o^8/5 (M_o/M_Jo)^2/15 r_o the coalescence time is shorter than the free-fall time and no fragmentation is possible below this radius. In the primordial clouds two major factors prevent fragmentation at larger radii. First, the background radiation is still ‘hot’ and the trapping of it would prevent fragmentation until the whole cloud has collapsed to a radius 10⁻² x^−2/3 r_o. Here x = 10⁻²(M/10⁷ M_⊙)^1/3 is the ionization fraction given by the balance between gravitational contraction and recombination cooling. Furthermore, any small density fluctuation would lead to fragmentation only after the paternal cloud had collapsed by a factor (δ/5)^2/3 in radius. For these reasons fragmentation is unlikely until centrifugal forces halt the collapse and a disk forms. The disk will be initially at T ≃ 10⁴K but after a small fraction of H₂ forms it will cool to T₃ ≃ T/10³K ≃ 1 and the final fragments mass could be as low as ≃ 0.2(λ_o/0.07)⁴ T₃²(M_Jo/M_o)^1/3 M_⊙.