Gravitational Instability in Collisionless Cosmological Pancakes
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The gravitational instability of cosmological pancakes composed of
collisionless dark matter in an Einstein-de Sitter universe is investigated
numerically to demonstrate that pancakes are unstable with respect to
fragmentation and the formation of filaments. A ``pancake'' is defined here as
the nonlinear outcome of the growth of a 1D, sinusoidal, plane-wave, adiabatic
density perturbation. We have used high resolution, 2D, N-body simulations by
the Particle-Mesh (PM) method to study the response of pancakes to perturbation
by either symmetric (density) or antisymmetric (bending or rippling) modes,
with corresponding wavevectors k_s and k_a transverse to the wavevector k_p of
the unperturbed pancake plane-wave. We consider dark matter which is initially
``cold'' (i.e. with no random thermal velocity in the initial conditions). We
also investigate the effect of a finite, random, isotropic, initial velocity
dispersion (i.e. initial thermal velocity) on the fate of pancake collapse and
instability. Pancakes are shown to be gravitationally unstable with respect to
all perturbations of wavelength l