Difficulties with Recovering the Masses of Supermassive Black Holes from Stellar Kinematical Data

Accepted for publication in the Astrophysical Journal We investigate the ability of three-integral, axisymmetric, orbit-based modeling algorithms to recover the parameters defining the gravitational potential (mass-to-light ratio Υ and black hole mass M•) in spheroidal stellar systems using stellar kinematical data. We show that the potential estimation problem is generically under-determined when applied to long-slit kinematical data of the kind used for most black hole mass determinations to date. A range of parameters (Υ, M•) can provide equally good fits to the data, making it impossible to assign best-fit values. The indeterminacy arises from the large variety of orbital solutions that are consistent with a given mass model. We demonstrate the indeterminacy using a variety of data sets derived from realistic models as well as published observations of the galaxy M32. The indeterminacy becomes apparent only when a sufficiently large number of distinct orbits are supplied to the modeling algorithm; if too few orbits are used, spurious minima appear in the χ 2 (Υ, M•) contours, and these minima do not necessarily coincide with the parameters defining the gravitational potential. We show that the range of degeneracy in M • depends on the degree to which the data resolve the radius

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