Spin parameter and scale-free density perturbations in hierarchical clustering

Details Spin parameter and scale-free density perturbations in hierarchical clustering Spin parameter and scale-free density perturbations in hierarchical clustering

Nov 1993

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993ap%26ss.209....1c&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 209, no. 1, p. 1-17

Astronomy and Astrophysics

Astrophysics

4

Astronomical Models, Density Distribution, Galactic Clusters, Galactic Evolution, Perturbation, Scale (Ratio), Spin, Angular Momentum, Anisotropy, Dark Matter, Ellipsoids, Elliptical Galaxies, Many Body Problem, Mass, Mathematical Models, Missing Mass (Astrophysics), Radii, Velocity Distribution

Scientific paper

The present attempt aims to predict the dependence of the spin parameter, lambda, the angular momentum, J, and the typical radius, avir, on the mass, M, which have been found in N-body simulations of extending density perturbations in hierarchical clustering, when virialization is attained. We show that lambda varies as M0 for systems with same adimensional density distribution and velocity distribution, and in particular for scale-free density perturbations in hierarchical clustering. In the special case of ellipsoidal perturbations, it is also found: J varies as M74, avir varies as M1/2. All these results turn out to be in close agreement with N-body simulations, despite the simple model adopted. Virialized ellipsoidal configurations with same energy and angular momentum are derived, and the dependence of the spin parameter on the anisotropy parameter, zetapec is investigated. Turning our attention to the formation galaxies, we derive the total mass as a function of the collapse factor, using the empirical anticorrelation between dark to visible mass ratio within the optical radius of disk galaxies and their luminous masses. Observational data related to a sample of elliptical galaxies provide evidence that the contraction in these bodies occurred in proportion to the square root of the ratio of total to luminous mass. On the contrary, it is deduced that dissipation of angular momentum in elliptical galaxies occurred more or less at the same rate. If both shape and anisotropy parameter are preserved during the collapse, typical axis ratios epsilon21 = 0.98, epsilon31 = 0.69, are found to correspond to a moderate anisotropy, zetapec approximately equals 0.27, with a small dependence on the spin parameter in the range allowed.

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