Resolving the mass--anisotropy degeneracy of the spherically symmetric
  Jeans equation I: theoretical foundation
  A widely employed method for estimating the mass of stellar systems with
apparent spherical symmetry is dynamical modelling using the spherically
symmetric Jeans equation. Unfortunately this approach suffers from a degeneracy
between the assumed mass density and the second order velocity moments. This
degeneracy can lead to significantly different predictions for the mass content
of the system under investigation, and thus poses a barrier for accurate
estimates of the dark matter content of astrophysical systems. In a series of
papers we describe an algorithm that removes this degeneracy and allows for
unbiased mass estimates of systems of constant or variable mass-to-light ratio.
The present contribution sets the theoretical foundation of the method that
reconstructs a unique kinematic profile for some assumed free functional form
of the mass density. The essence of our method lies in using flexible B-spline
functions for the representation of the radial velocity dispersion in the
spherically symmetric Jeans equation. We demonstrate our algorithm through an
application to synthetic data for the case of an isotropic King model with
fixed mass-to-light ratio, recovering excellent fits of theoretical functions
to observables and a unique solution. The mass-anisotropy degeneracy is removed
to the extent that, for an assumed functional form of the potential and mass
density pair $(\Phi,\rho)$, and a given set of line-of-sight velocity
dispersion $\sigma_{los}^2$ observables, we recover a unique profile for
$\sigma_{rr}^2$ and $\sigma_{tt}^2$. Our algorithm is simple, easy to apply and
provides an efficient means to reconstruct the kinematic profile.
