An Analytical Approach to the Spin Distribution of Dark Halos

We derive the distribution of the dimensionless specific angular momentum of dark matter halos, P (j), in the framework of the standard tidal torque theory, and explain the characteristic shape of P (j) commonly observed in N-body simulations. A scalar quantity (shear scalar), r, is introduced for measuring the effective strength of the tidal torque force acting upon the halo from the surrounding matter. It is found that the ubiquitous and broad shape of P (j) can mostly be attributed to the unique property of the shear scalar r, and also that P (j) is insensitve to the underlying collapse dynamics. Our result demonstrates that although the shape of P (j) is ubiquitous and close to log-normal, the distribution is not exactly log-normal but decays exponentially at the high angular momentum end, and drops slowly as a power-law with an index 2 at the low angular momentum end. Subject headings: cosmology:theory — large-scale structure of universe