On the properties of elliptical and spiral galaxies in a CDM scenario

This paper aims to investigate what kind of density perturbations did lead to elliptical galaxies and what kind to spiral galaxies, in the context of a CDM scenario. Previous work by HP (Heavens and Peacock, 1988) is reviewed and extended; more particularly: (i) a theoreticalJM relation is derived for virialized configurations, with a slope increasing with the mass, in the range 5/3<<2, and compared with its counterpart deduced by HP for expanding configurations; (ii) an non-dimensional angular momentum =J/(G ² M ⁵ t _ff )^1/3; witht _ff free-fall time at turnaround, is calculated explicitly and compared with the usual spin parameter =J(–E) ^1/2/(GM ^5/2), in the special case of polytropic spheres and for different peak heights; (iii) a model is built up where the ellipsoidal density perturbations described by HP are approximated as spherical density perturbations with the same mass and the same rate of acquisition of angular momentum, and the contribution of the latter to the expansion is also taken into account. The calculations are limited to the special case of Einstein-de Sitter universes (of dust only), in the whole range of HP distributions of angular momenta. If a massM=10¹² m is typical for galaxies, the results are consistent with both an inferred difference roughly in a factor of six times between angular momenta of ellipticals and spirals, and a continuous transition from the former to the latter, for each peak height. It is argued that star formation together with angular momentum, instead of peak height alone, makes the fate of a given proto-object; more specifically, if star formation is high enough and/or angular momentum is low enough, the system will be frozen as an elliptical galaxy; if, on the other hand, the rate of star formation is low enough, and/or angular momentum is high enough, the system will be frozen as a spiral galaxy. In addition, the results lead to an obvious trend: more ellipticals are associated with higher peak heights and more spirals with lower peak heights.