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Abstract: General criteria to check the positivity of the distribution functionphase-space consistency of stellar systems of assigned density and anisotropyprofile are useful starting points in Jeans-based modeling. Here wesubstantially extend previous results, and we present the inversion formula andthe analytical necessary and sufficient conditions for phase-space consistencyof the family of multi-component Cuddeford spherical systems: the distributionfunction of each density component of these systems is defined as the sum of anarbitrary number of Cuddeford distribution functions with arbitrary values ofthe anisotropy radius, but identical angular momentum exponent. The radialtrend of anisotropy that can be realized by these models is therefore verygeneral. As a surprising by-product of our study, we found that the ``centralcusp-anisotropy theorem- a necessary condition for consistency relating thevalues of the central density slope and of the anisotropy parameter holds notonly at the center, but at all radii in consistent multi-component generalizedCuddeford systems. This last result suggests that the so-calledmass-anisotropy degeneracy could be less severe than what is sometimes feared.



Author: Luca Ciotti 1, Lucia Morganti 1,2 1 Astronomy dept. Bologna University - 2 MPE Garching

Source: https://arxiv.org/



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