An analytical model for the triaxial collapse of cosmological perturbations
Eisenstein, Daniel J.
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CitationEisenstein, Daniel J., and Abraham Loeb. 1995. “An Analytical Model for the Triaxial Collapse of Cosmological Perturbations.” The Astrophysical Journal 439 (February): 520. https://doi.org/10.1086/175193.
AbstractWe present an analytical model for the nonspherical collapse of overdense regions out of a Gaussian random field of initial cosmological perturbations. The collapsing region is treated as an ellipsoid of constant density, acted upon by the quadrupole tidal shear from the surrounding matter. The dynamics of the ellipsoid is set by the ellipsoid self-gravity and the external quadrupole shear. Both forces are linear in the coordinates and therefore maintain homogeneity of the ellipsoid at all times. The amplitude of the external shear is evolved into the nonlinear regime in thin spherical shells that are allowed to move only radially according to the mass interior to them. The full dynamical equations then reduce to a set of nine second-order ordinary differential equations, which reproduce the linear regime behavior but can be evolved past turnaround, well into the nonlinear regime. We describe how the initial conditions can be drawn in the appropriate correlated way from a random field of initial density perturbations. The model is applied to a restricted set of initial conditions that are more suitable to the above approximations; most notably we focus on the properties of rare high-density peaks (greater than or similar to 2 sigma). By considering many random realizations of the initial conditions, we calculate the distribution of shapes and angular momenta acquired by objects through the coupling of their quadrupole moment to the tidal shear. The average value of the spin parameter, (lambda) approximate to 0.04, is found to be only weakly dependent on the system mass, the mean cosmological density, or the initial power spectrum of perturbations, in agreement with N-body simulations. For the cold dark matter power spectrum, most objects evolve from a quasi-spherical initial state to a pancake or filament and then to complete virialization. Low-spin objects tend to be more spherical. The evolution history of shapes is primarily induced by the external shear and not by the initial triaxiality of the objects. The statistical distribution of the triaxial shapes of collapsing regions can be used to test cosmological models against galaxy surveys on large scales.
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