The Caustic Ring Model of the Milky Way Halo

We present a proposal for the full phase space distribution of the Milky Way halo. The model is axially and reflection symmetric and its time evolution is self-similar. It describes the halo as a set of discrete dark matter flows with stated densities and velocity vectors everywhere. We first discuss the general conditions under which the time evolution of a cold collisionless self-gravitating fluid is self-similar, and show that symmetry is not necessary for self-similarity. When spherical symmetry is imposed, the model is the same as described by Fillmore and Goldreich, and by Bertschinger, twenty-three years ago. The spherically symmetric model depends on one dimensionless parameter $\epsilon$ and two dimensionful parameters. We set $\epsilon$ = 0.3, a value consistent with the slope of the power spectrum of density perturbations on galactic scales. The dimensionful parameters are determined by the Galactic rotation velocity (220 km/s) at the position of the Sun and by the age of the Galaxy (13.7 Gyr). The properties of the outer caustics are derived in the spherically symmetric model. The structure of the inner halo depends on the angular momentum distribution of the dark matter particles. We assume that distribution to be axial and reflection symmetric, and dominated by net overall rotation. The inner caustics are rings whose radii are determined in terms of a single additional parameter $j_{\rm max}$. We summarize the observational evidence in support of the model. The evidence is consistent with $j_{\rm max}$ = 0.18 in Concordance Cosmology, equivalent to $j_{\rm max,old}$ = 0.26 in Einstein - de Sitter cosmology. We give formulas to estimate the flow densities and velocity vectors anywhere in the Milky Way halo. The properties of the first forty flows at the location of the Earth are listed.