1305.0497 (Christian Angrick)

Ellipticity and prolaticity of the initial gravitational-shear field at the position of density maxima    [PDF]

Christian Angrick

Dark-matter haloes are supposed to form at the positions of maxima in the initial matter density field. The gravitational-shear field's ellipticity and prolaticity that serve as input for the ellipsoidal-collapse model, however, are derived from a distribution that does not take the additional maximum constraint into account. In this article, I quantify the variations of the most probable and the expected values of the ellipticity and the prolaticity when considering this additional constraint. Based on the statistics of Gaussian random fields, it is possible to set up a joint distribution for the eigenvalues of the gravitational-shear tensor and the matter density that incorporates the maximum constraint by invoking a vanishing first derivative and a negative definite second derivative of the density field into the calculation. Both the most probable and the expected value of the ellipticity calculated under the assumption of a density maximum are about 1-8 % lower compared to the standard distribution used in the literature in the density range relevant for cosmological structure formation. Additionally, the analogous quantities for the prolaticity do not vanish but acquire slight positive values in the range of 10^{-7} to 10^{-2}. For large overdensities, the predictions from both distributions converge. The non-vanishing prolaticity may have consequences for the ellipsoidal-collapse model especially when the linear model for the external shear is used.

View original: http://arxiv.org/abs/1305.0497