Kinematic deprojection and mass inversion of spherical systems of known velocity anisotropy - Astrophysics > Cosmology and Nongalactic AstrophysicsReport as inadecuate




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Abstract: Traditionally, the mass - velocity anisotropy degeneracy MAD inherent inthe spherical, stationary, non-streaming Jeans equation has been handled byassuming a mass profile and fitting models to the observed kinematical data.Here, the opposite approach is considered: the equation of anisotropickinematic projection is inverted for known arbitrary anisotropy to yield thespace radial velocity dispersion profile in terms of an integral involving theradial profiles of anisotropy and isotropic dynamical pressure. Then, throughthe Jeans equation, the mass profile is derived in terms of double integrals ofobservable quantities. Single integral formulas for both deprojection and massinversion are provided for several simple anisotropy models isotropic, radial,circular, general constant, Osipkov-Merritt, Mamon-Lokas andDiemand-Moore-Stadel. Tests of the mass inversion on NFW models with theseanisotropy models yield accurate results in the case of perfect observationaldata, and typically better than 70% in 4 cases out of 5 accurate massprofiles for the sampling errors expected from current observational data onclusters of galaxies. For the NFW model with mildly increasing radialanisotropy, the mass is found to be insensitive to the adopted anisotropyprofile at 7 scale radii and to the adopted anisotropy radius at 3 scale radii.This anisotropic mass inversion method is a useful complementary tool toanalyze the mass and anisotropy profiles of spherical systems. It provides thepractical means to lift the MAD in quasi-spherical systems such as globularclusters, round dwarf spheroidal and elliptical galaxies, as well as groups andclusters of galaxies, when the anisotropy of the tracer is expected to belinearly related to the slope of its density.



Author: Gary A. Mamon 1,2, Gwenael Boué 1,3 1 IAP CNRS and UPMC, 2 Astrophysics and BIPAC, Univ. of Oxford, 3 IMCCE Obs. de Paris, CNRS

Source: https://arxiv.org/



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