An Analytical Approach to the Spin Distribution of Dark Halos

We derive the distribution of the dimensionless specific angular momentum ofdark matter halos, $P(j)$, in the framework of the standard tidal torquetheory, and explain the characteristic shape of $P(j)$ commonly observed inN-body simulations. A scalar quantity (shear scalar), $r$, is introduced formeasuring the effective strength of the tidal torque force acting upon the halofrom 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. Ourresult demonstrates that although the shape of $P(j)$ is ubiquitous and closeto log-normal, the distribution is not exactly log-normal but decaysexponentially at the high angular momentum end, and drops slowly as a power-lawwith an index 2 at the low angular momentum end.Comment: 14 pages including two figures, submitted to ApJ Let