The Role of Hydrogen Molecules in the Radiative Cooling and Fragmentation of Cosmological Sheets

We extend previous studies of nonlinear hydrodynamical effects on the fragmentation of cosmological sheets in a dark matter dominated universe by allowing for the formation of hydrogen molecules. This is accomplished by solving a reaction flow system in nonequilibrium for the baryonic fluid that includes 27 chemical reactions and nine separate species: H, H⁺, He, He⁺, He⁺⁺, H⁻, H₂⁺, H₂, and e⁻. Several one-dimensional calculations are performed for different initial data parameterized by the perturbation wavelength λ₁ along the collapsing direction. Initial wavelengths in the range 1-10 Mpc corresponding to average shock velocities of 9-110 km s⁻¹ are considered. The higher velocity shocks produce higher concentrations of molecular hydrogen ranging from nH2 = 5.8 × 10⁻² cm⁻³ with a mass fraction nH2/n = 2.8 × 1O⁻³ for the 10 Mpc case to 2.5 × 10⁻⁷ and 1.5 × 10⁻⁵ for λ₁ = 1 Mpc. The gas for those shocks (namely λ₁ > 1 Mpc) that produces large concentrations of H₂ then cools further through the vibrational/rotational excitation of the molecules. For the λ₁ = 10 Mpc case, the temperature drops to 4.3 × 10⁻³ eV at redshift z = 4.4, where H₂ peaks in concentration. This is compared to 0.19 eV in a six species model for which H⁻, H2⁺, and H₂⁺ are neglected. However, as the shock speed is decreased, the H₂ formation time increases and for the 1 Mpc case H₂ does not form rapidly enough to compensate for the decrease in the density because of the cosmological expansion and hence cannot affect the cooling of the gas. Because the cooling is isobaric, the accompanying increase in density together with the drop in temperature combine to collapse the gas to smaller volumes and to reduce the Jeans mass by factors ranging from 10³ for λ₁ = 10 Mpc (dropping from 9 x 10⁶ Msun when H₂ is neglected to 9 x 1O³ Msun) to nearly unity for λ₁ = 1 Mpc. Hence, the faster moving shocks are likely to fragment into smaller units that may be associated with massive stars. The fragmentation process is investigated with two-dimensional simulations for the case λ₁ = 4 Mpc. We confirm predictions from the one-dimensional studies regarding the size and mass estimates of fragments.