The formation of pregalactic objects from white-noise density perturbations

We investigate the general case of baryonic collapse in a universe dominated by cold dark matter with a white-noise fluctuation spectrum δρ/ρ = (M/M₀)^-1/2. For Ω = 1 and Ω_bh² = 0.02, baryonic collapse from molecular cooling requires a minimum fluctuation mass of M₀ = 0.12h^-4.4 M_⊙ ; below this mass, baryons can collapse out of the Hubble flow and virialize, but the formation of compact objects is impossible. This requirement produces a minimum redshift for the formation of pregalactic objects from white-noise perturbations: 1 + z > 16. The minimum baryonic mass which can cool and collapse into bound objects is M = 4000 M_⊙ h^-2.4. As a specific example, we examine white-noise fluctuations in the axion field.