MAMPOSSt: Modelling Anisotropy and Mass Profiles of Observed Spherical
  Systems. I. Gaussian 3D velocities
  Mass modelling of spherical systems through internal motions is hampered by
the mass/velocity anisotropy (VA) degeneracy inherent in the Jeans equation, as
well as the lack of techniques that are both fast and adaptable to realistic
systems. A new fast method, called MAMPOSSt, which performs a maximum
likelihood fit of the distribution of observed tracers in projected phase
space, is developed and thoroughly tested. MAMPOSSt assumes a shape for the
gravitational potential, but instead of postulating a shape for the
distribution function in terms of energy and angular momentum, or supposing
Gaussian line-of-sight velocity distributions, MAMPOSSt assumes a VA profile
and a shape for the 3D velocity distribution, here Gaussian. MAMPOSSt requires
no binning, differentiation, nor extrapolation of the observables. Tests on
cluster-mass haloes from LambdaCDM cosmological simulations show that, with 500
tracers, MAMPOSSt is able to jointly recover the virial radius, tracer scale
radius, dark matter scale radius and outer or constant VA with small bias (<10%
on scale radii and <2% on the two other quantities) and inefficiencies of 10%,
27%, 48% and 20%, respectively. MAMPOSSt does not perform better when some
parameters are frozen, and even worse when the virial radius is set to its true
value, which appears to be the consequence of halo triaxiality. The accuracy of
MAMPOSSt depends weakly on the adopted interloper removal scheme, including an
efficient iterative Bayesian scheme that we introduce here, which can directly
obtain the virial radius with as good precision as MAMPOSSt. Our tests show
that MAMPOSSt with Gaussian 3D velocities is very competitive with, and up to
1000x faster than other methods. Hence, MAMPOSSt is a very powerful and rapid
tool for the mass and anisotropy modeling of systems such as clusters and
groups of galaxies, elliptical and dwarf spheroidal galaxies.
