On the spin parameter of dark-matter haloes

Matthias Steinmetz; Matthias Bartelmann

doi:10.1093/mnras/272.3.570

paper

On the spin parameter of dark-matter haloes

arXiv:astro-ph/9403017 · doi:10.1093/mnras/272.3.570

Abstract

The study by White (1984) on the growth of angular momentum in dark haloes is extended towards a more detailed investigation of the spin parameter $λ \equiv L E / G M^{2.5}$ . Starting from the Zel'dovich approximation to structure formation, a dark halo is approximated by a homogeneous ellipsoid with the inertial tensor of the (highly irregular) Lagrangian region $Υ$ from which the dark halo forms. Within this approximation, an expression for the spin parameter can be derived, which depends on the geometry of $Υ$ , the cosmological density parameter $Ω_{0}$ , the overdensity of the dark halo, and the tidal torque exerted on it. For Gaussian random fields, this expression can be evaluated statistically. As a result, we derive a probability distribution of the spin parameter which gives $λ ≃ 0.0 7_{- 0.05}^{+ 0.04}$ , consistent with numerical investigations. This probability distribution steeply rises with increasing spin parameter, reaching its maximum at $λ ≃ 0.025$ . The 10 (50,90) percentile values are $λ = 0.02$ (0.05,0.11, respectively). There is a weak anticorrelation of the spin parameter with the peak height $ν$ of the density fluctuation field $λ \propto ν^{- 0.29}$ . The dependence on $Ω_{0}$ and the variance $σ$ of the density-contrast field is very weak; there is only a marginal tendency for the spin parameter to be slightly larger for late-forming objects in an open universe. Due to the weak dependence on $σ$ , our results should be quite generally applicable and independent on

16 pages, preprint MPA 794

On the spin parameter of dark-matter haloes

Abstract

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