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.Comment: 21 pages, 15 figures. Accepted by MNRAS. Typo corrected in eq. 3

Line-of-sight velocity dispersions and a mass distribution model of the Sa galaxy NGC 4594

In the present paper we develop an algorithm allowing to calculate line-of-sight velocity dispersions in an axisymmetric galaxy outside of the galactic plane. When constructing a self-consistent model, we take into account the galactic surface brightness distribution, stellar rotation curve and velocity dispersions. This algorithm is applied to a Sa galaxy NGC 4594 = M 104, for which there exist velocity dispersion measurements outside of the galactic major axis. The mass distribution model is constructed in two stages. In the first stage we construct a luminosity distribution model, where only galactic surface brightness distribution is taken into account. Thereafter, in the second stage we develop on the basis of the Jeans equations a detailed mass distribution model and calculate line-of-sight velocity dispersions and the stellar rotation curve. Here a dark matter halo is added to visible components. Calculated dispersions are compared with observations along different slit positions perpendicular and parallel to the galactic major axis. In the best-fitting model velocity dispersion ellipsoids are radially elongated. Outside the galactic plane velocity dispersion behaviour is more sensitive to the dark matter density distribution and allows to estimate dark halo parameters.Comment: 12 pages, 13 figures, accepted for publication in MNRA