4.6 Cosmological sheets

Cosmological sheets, or pancakes, form as overdense regions collapse preferentially along one axis. Originally studied by Zel’dovich [165Jump To The Next Citation Point] in the context of neutrino-dominated cosmologies, sheets are ubiquitous features in nonlinear structure formation simulations of CDM-like models with baryonic fluid, and manifest on a spectrum of length scales and formation epochs. Gas collapses gravitationally into flattened sheet structures, forming two plane parallel shock fronts that propagate in opposite directions, heating the infalling gas. The heated gas between the shocks then cools radiatively and condenses into galactic structures. Sheets are characterized by essentially five distinct components: the preshock inflow, the postshock heated gas, the strongly cooling/recombination front separating the hot gas from the cold, the cooled postshocked gas, and the unshocked adiabatically compressed gas at the center. Several numerical calculations [4714522] have been performed of these systems which include baryonic fluid with hydrodynamical shock heating, ionization, recombination, dark matter, thermal conductivity, and radiative cooling (Compton, bremsstrahlung, and atomic line cooling), in both one and two spatial dimensions to assert the significance of each physical process and to compute the fragmentation scale. See also [16] where fully general relativistic numerical calculations of cosmological sheets are presented in plane symmetry, including relativistic hydrodynamical shock heating and consistent coupling to spacetime curvature.

In addition, it is well known that gas which cools to 1 eV through hydrogen line cooling will likely cool faster than it can recombine. This nonequilibrium cooling increases the number of electrons and ions (compared to the equilibrium case) which, in turn, increases the concentrations of H − and + H 2, the intermediaries that produce hydrogen molecules H2. If large concentrations of molecules form, excitations of the vibrational/rotational modes of the molecules can efficiently cool the gas to well below 1 eV, the minimum temperature expected from atomic hydrogen line cooling. Because the gas cools isobarically, the reduction in temperature results in an even greater reduction in the Jeans mass, and the bound objects which form from the fragmentation of H 2 cooled cosmological sheets may be associated with massive stars or star clusters. Anninos and Norman [18] have carried out 1D and 2D high resolution numerical calculations to investigate the role of hydrogen molecules in the cooling instability and fragmentation of cosmological sheets, considering the collapse of perturbation wavelengths from 1 Mpc to 10 Mpc. They find that for the more energetic (long wavelength) cases, the mass fraction of hydrogen molecules reaches −3 nH2 ∕nH ∼ 3 × 10, which cools the gas to − 3 4 × 10 eV and results in a fragmentation scale of 9 × 103 M ⊙. This represents reductions of 50 and 103 in temperature and Jeans mass respectively when compared, as in Figure 12View Image, to the equivalent case in which hydrogen molecules were neglected.

However, the above calculations neglected important interactions arising from self-consistent treatments of radiation fields with ionizing and photo-dissociating photons and self-shielding effects. Susa and Umemura [153] studied the thermal history and hydrodynamical collapse of pancakes in a UV background radiation field. They solve the radiative transfer of photons together with the hydrodynamics and chemistry of atomic and molecular hydrogen species. Although their simulations were restricted to one-dimensional plane parallel symmetry, they suggest a classification scheme distinguishing different dynamical behavior and galaxy formation scenarios based on the UV background radiation level and a critical mass corresponding to 1 − 2σ density fluctuations in a standard CDM cosmology. These level parameters distinguish galaxy formation scenarios as they determine the local thermodynamics, the rate of H2 line emissions and cooling, the amount of starburst activity, and the rate and mechanism of cloud collapse.

View Image

Figure 12: Two different model simulations of cosmological sheets are presented: a six species model including only atomic line cooling (left), and a nine species model including also hydrogen molecules (right). The evolution sequences in the images show the baryonic overdensity and gas temperature at three redshifts following the initial collapse at z = 5. In each figure, the vertical axis is 32 kpc long (parallel to the plane of collapse) and the horizontal axis extends to 4 Mpc on a logarithmic scale to emphasize the central structures. Differences in the two cases are observed in the cold pancake layer and the cooling flows between the shock front and the cold central layer. When the central layer fragments, the thickness of the cold gas layer in the six (nine) species case grows to 3 (0.3) kpc and the surface density evolves with a dominant transverse mode corresponding to a scale of approximately 8 (1) kpc. Assuming a symmetric distribution of matter along the second transverse direction, the fragment masses are approximately 107 (105) solar masses.

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