On the reliability of the black hole mass and mass to light ratio determinations with Schwarzschild models

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Abstract
In this Letter, we investigate the claim of Valluri et al. (2003), namely that the use of Schwarzschild dynamical (orbit-based) models leads to an indeterminacy regarding the estimation of the free parameters like the central black hole mass and the stellar mass-to-light ratio of the galaxy under study. We examine this issue with semi-analytic two-integral models, which are not affected by the intrinsic degeneracy of three-integral systems. We however confirm the Valluri et al. result, and observe the so-called widening of the chi2 contours as the orbit library is expanded. We also show that, although two-dimensional data coverage help in constraining the orbital structure of the modelled galaxy, it does not in principle solve the indeterminacy issue, which mostly originates from the discretization of such an inverse problem. We show that adding regularization constraints stabilizes the confidence level contours on which the estimation of black hole mass and stellar mass-to-light ratio are based. We therefore propose to systematically use regularization as a tool to prevent the solution to depend on the orbit library. Regularization, however, introduces an unavoidable bias on the derived solutions. We hope that the present Letter will trigger some more research directed at a better understanding of the issues addressed here.

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