Tidal torques and local density maxima

We have calculated the distribution of tidal torques acting on matter in the neighbourhood of local density maxima when the density perturbations are small. We find that high peaks experience higher torques than low peaks. The higher torques acting on the high peaks are counteracted by the shorter collapse time during which the torques can act. Which effect is dominant depends on the perturbation power spectrum: for power spectra characteristic of both cold dark matter and hot dark matter, the effects nearly cancel, and the total angular momentum acquired by a collapsing object is almost independent of the height of the peak. Furthermore, the distributions of angular momenta acquired by collapsing protosystems are extremely broad, for all power spectra; the range of angular momenta of peaks of a given height far exceeds any modest systematic differences between peaks of different height. We have also calculated the distribution of λ – the dimensionless spin parameter – for density maxima. This quantity has a median value λ≃0.05 with no strong dependence on power spectrum, in good agreement with N-body simulations. Unlike total angular momentum, λ does show an anticorrelation with peak height, but again the distributions are very broad by comparison with the systematic shift. These results indicate that it is not possible to account for the systematic differences in angular momentum properties of disc and elliptical galaxies simply by postulating that the latter arise from fluctuations of greater overdensity, contrary to some recent suggestions.