Three-dimensional hydrodynamical calculations on the fragmentation of pancakes and galaxy formation

The fragmentation of pancakes is numerically investigated by a three- dimensional smoothed particle hydrodynamics (SPH) combined with a usual N-body scheme, where the ionization equilibria are solved and all kinds of the cooling and heating processes are explicitly included for primordial gas. We consider dark-matter-dominated pancakes as well as baryon-dominated ones, in a range of pancake mass Mₚan_ = 10¹3-15^ Mₛun_. We find a three-step fragmentation scenario: First, the fragmentation is triggered by the filamentary mode instability in a central cooled dense layer. Second, they are torn to numerous lumps, forming chainlike structures. Finally, the lumps flow toward the outer edge, and a central hole develops. Then the lumps collide with each other and merge into larger ones. The final stage of hole making may lead to a kind of dynamical antibiasing in the sense that galaxies eventually form far away from peaks of initial density fluctuations. In the present simulations, the galaxy formation efficiency is as small as fGF_~ exp -2 (Mₚan_/10¹4^ Mₛun_) ¹/5^. Some characteristic properties are presented in relation to galaxy formation. The typical mass of fragments is proportional to the pancake mass as Mb_ ~ 0. 3-2 x 10¹1^ Mₛun_ (Mₚan_/10¹4^ Mₛun_) in baryons, and the rotation velocity inferred from the mass and size of each fragment is Vᵣot_~ 140-230 km s^-1^ (Mₚan_/10¹4^ Mₛun_) ¹/3^. The H i column density of an edge-on pancake is typically NHI_~1. 4 x 10²1^ cm^-2^ (Mₚan_/10¹4^ Mₛun_) ¹/3^, and those of fragments are in the range 10²0-20. 7^ cm^-2^ (Mₚan_/10¹4^ Mₛun_) ¹/3^ at Z ~ 2, which can be compared to the damped Lyα absorption systems at the high redshifts. The properties we obtain are consistent with the recently discovered Z = 3. 4 pancake. Other quantities such as the specific angular momenta and the line of sight relative peculiar velocity dispersion are also presented. As for the shock-heated hot intergalactic gas, some estimates are made for X-ray luminosities, the Sunyaev-Zel'dovich effect, and the Compton γ-parameter. The fragmentation process turns out to be strongly dependent upon imposed small-scale fluctuations. Unless there are some small-scale seed fluctuations imposed, the pancakes will not fragment. Therefore, a hot dark matter (HDM) dominated universe does not seem preferable as a complete model of galaxy formation. It is found that just a small fluctuation amplitude is required for fragmentation at smaller scales than the HDM free-streaming damping mass. A two-component dark-matter- dominated universe turns out to be successful from a viewpoint of galaxy formation.