Collapse of population III objects

Starting from the recombination era, we investigate the cooling and collapse of Population III objects for masses M∼M_J and M≪M_J where M_J, is the Jeans mass at the beginning of the recombination era. We take into account not only the internal pressure of the cloud, but also photon cooling, photon drag, photoionization by the background radiation, collisional ionization, and a complete set of equations for the formation and destruction of the hydrogen molecule. For M−M_J, we assume an isothermal density fluctuation spectrum suggested by Gott & Rees: δϱ/ϱ = (M/M₀)^−1/3/(1 + z_rec), where z_rec is the recombination redshift and M₀ defines the mass-scale, which we take as a galactic cluster =$$10^{15}M_\odot$$ . Assuming $$\Omega h^2=0.1$$, our numerical solutions show: (i) the first bound systems were $$\sim10^{15}M_\odot$$; (ii) the collapse of the clouds were not significantly delayed by the internal pressure of the cloud (since at turn-around, the cloud’s temperature is close to the ambient temperature). After turn-around, when the radius of the cloud has decreased to 1/2 its value at turn-around; (iii) the temperature does not rise adiabatically (e.g. $$T/T_\text{ad}=0.73$$ for $$M=10^6M_\odot$$); (iv) the concentration of hydrogen molecules remains low (e.g. $$n_{\text H_2}/n=3.0\times10^{-12}$$ for $$M=10^6M_\odot$$); and (v) the fractional ionization does not become small (e.g. $$n_\text e/n=2.4\times10^{-5}$$ for $$M=10^6M_\odot$$). We evaluate numerically the delay of isothermal density fluctuations of mass M≪M_J during the recombination era due to the non-sudden elimination of dynamical coupling with the radiation and the gradual loss of thermal contact with it. We find, in general, that $$\delta_f/\delta_\text i$$, is not negligible, where (l + δ)ϱ is the central density of the fluctuation, ϱ is the ambient density and $$\delta_\text i(\delta_\text f)$$ is the initial (end) of recombination era value of δ. We find for $$M/M_\text J=0.001$$, $$\Omega h^2=1.0$$ and $$\delta_\text i=0.01-1.0$$, for example, $$\delta_\text f/\delta_\text i\simeq40-50$$ percent.