MAMPOSSt: Modelling Anisotropy and Mass Profiles of Observed Spherical Systems – I. Gaussian 3D velocities

Abstract

Mass modelling of spherical systems through internal motions is hampered by\nthe mass/velocity anisotropy (VA) degeneracy inherent in the Jeans equation, as\nwell as the lack of techniques that are both fast and adaptable to realistic\nsystems. A new fast method, called MAMPOSSt, which performs a maximum\nlikelihood fit of the distribution of observed tracers in projected phase\nspace, is developed and thoroughly tested. MAMPOSSt assumes a shape for the\ngravitational potential, but instead of postulating a shape for the\ndistribution function in terms of energy and angular momentum, or supposing\nGaussian line-of-sight velocity distributions, MAMPOSSt assumes a VA profile\nand a shape for the 3D velocity distribution, here Gaussian. MAMPOSSt requires\nno binning, differentiation, nor extrapolation of the observables. Tests on\ncluster-mass haloes from LambdaCDM cosmological simulations show that, with 500\ntracers, MAMPOSSt is able to jointly recover the virial radius, tracer scale\nradius, dark matter scale radius and outer or constant VA with small bias (<10%\non scale radii and <2% on the two other quantities) and inefficiencies of 10%,\n27%, 48% and 20%, respectively. MAMPOSSt does not perform better when some\nparameters are frozen, and even worse when the virial radius is set to its true\nvalue, which appears to be the consequence of halo triaxiality. The accuracy of\nMAMPOSSt depends weakly on the adopted interloper removal scheme, including an\nefficient iterative Bayesian scheme that we introduce here, which can directly\nobtain the virial radius with as good precision as MAMPOSSt. Our tests show\nthat MAMPOSSt with Gaussian 3D velocities is very competitive with, and up to\n1000x faster than other methods. Hence, MAMPOSSt is a very powerful and rapid\ntool for the mass and anisotropy modeling of systems such as clusters and\ngroups of galaxies, elliptical and dwarf spheroidal galaxies.\n