NONLINEAR HYDRODYNAMICS OF COSMOLOGICAL SHEETS .2. FRAGMENTATION AND THE GRAVITATIONAL, COOLING, AND THIN-SHELL INSTABILITIES

Two-dimensional numerical simulations of cosmological sheets are carried out to investigate nonlinear hydrodynamical effects on the formation of structures such as protogalaxies in the universe. We follow the motion of both baryonic and dark matter in a postrecombination Friedmann model universe with Omega(0) = 1, Omega(b) = 0.1, and H-0 = 75 km s(-1) Mpc(-1) at scales (less than or equal to 10 Mpc) much smaller than the horizon size. We use a nonuniformly gridded code, composed of the Eulerian hydrodynamic solver ZEUS-2D modified for cosmology and a two-dimensional particle-mesh algorithm, to provide adequate resolution throughout the sheet structures. Our simulations allow us to examine in detail the role that nonlinear gravitational, cooling, and thin-shell instabilities play in the fragmentation of cosmological sheets. We compute characteristic fragmentation time and length scales for a variety of initial data and symmetries across the midplane. We find that although the fragmentation time is dependent on the power in the fluctuation spectrum, the average size of the protogalactic objects which form by the end of the fragmentation process (z greater than or similar to 2.4) is similar in all cases studied, ranging from 8 to 13 kpc in the plane of collapse with masses of the order of a few times 10(8) M. for both the baryonic and the dark matter. We also find that in relaxing reflection symmetry across the midplane, a thin-shell instability acts as early times to excite the bending modes of the cold layer at scales set by kL similar to 0.1, where k is the transverse wavenumber and L is the pancake thickness, significantly increasing the turbulence and local vorticity of the pancake.