  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.
