ON THE SPIN PARAMETER OF DARK-MATTER HALOES

The study by White on the growth of angular momentum in dark haloes is extended towards a more detailed investigation of the spin parameter lambda = L root E/GM(2.5). Starting from the Zel'dovich approximation to structure formation, a dark halo is approximated by a homogeneous e llipsoid with the inertial tenser of the (highly irregular) Lagrangian region Upsilon from which the dark halo forms. Within this approximat ion, an expression for the spin parameter can be derived, which depend s on the geometry of Upsilon, the cosmological density parameter Omega (0), the overdensity of the dark halo, and the tidal torque exerted on it. For Gaussian random fields, this expression can be evaluated stat istically. As a result, we derive a probability distribution of the sp in parameter which gives lambda similar or equal to 0.07(-0.05)(+0.04) , consistent with numerical investigations. This probability distribut ion steeply rises with increasing spin parameter, reaching its maximum at lambda similar or equal to 0.025. The 10 (50, 90) percentile value s are lambda = 0.02 (0.05, 0.11, respectively). There is a weak antico rrelation of the spin parameter with the peak height nu of the density fluctuation field, lambda proportional to nu(-0.29). The dependence o n Omega(0) and the variance sigma of the density-contrast field is ver y 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 sigma, our results should be quite generally ap plicable and independent of the special type of the fluctuation spectr um.