Analytical Solutions to the Mass-Anisotropy Degeneracy with Higher Order
  Jeans Analysis: A General Method
  The Jeans analysis is often used to infer the total density of a system by
relating the velocity moments of an observable tracer population to the
underlying gravitational potential. This technique has recently been applied in
the search for Dark Matter in objects such as dwarf spheroidal galaxies where
the presence of Dark Matter is inferred via stellar velocities. A precise
account of the density is needed to constrain the expected gamma ray flux from
DM self-annihilation and to distinguish between cold and warm dark matter
models. Unfortunately the traditional method of fitting the second order Jeans
equation to the tracer dispersion suffers from an unbreakable degeneracy of
solutions due to the unknown velocity anisotropy of the projected system. To
tackle this degeneracy one can appeal to higher moments of the Jeans equation.
By introducing an analog to the Binney anisotropy parameter at fourth order,
beta' we create a framework that encompasses all solutions to the fourth order
Jeans equations rather than those in the literature that impose unnecessary
correlations between anisotropy of second and fourth order moments. The
condition beta' = f(beta) ensures that the degeneracy is lifted and we
interpret the separable augmented density system as the order-independent case
beta'= beta. For a generic choice of beta' we present the line of sight
projection of the fourth moment and how it could be incorporated into a joint
likelihood analysis of the dispersion and kurtosis. Having presented the
mathematical framework, we then use it to develop a statistical method for the
purpose of placing constraints on dark matter density parameters from discrete
velocity data. The method is tested on simulated dwarf spheroidal data sets
leading to results which motivate study of real dwarf spheroidal data sets.
