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

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  • 17 October 2002
Abstract
We investigate the ability of three-integral, axisymmetric, orbit-based modelling algorithms to recover the parameters defining the gravitational potential (black hole mass M_h and stellar M/L) in spheroidal stellar systems using stellar kinematical data. We show that the potential estimation problem is generically under-determined: a range of parameters can provide equally good fits to the data, making it impossible to assign best-fit values. 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 modelling algorithm; if too few orbits are used, spurious minima appear in the chi-squared contours. In most cases these minima do not coincide with the parameters defining the gravitational potential. We show that the range of degeneracy in M_h depends strongly on the degree to which the data resolve the radius of influence R_h of the black hole. For FWHM/2R_h > 0.5, we find that only very weak constraints can be placed on M_h. In the case of M32, our reanalysis demonstrates that data published prior to 2000 (FWHM/2R_h ~ 0.25) are equally consistent with black hole masses in the range 1-6 million solar masses, with no preferred value in that range. We show that HST/STIS data for this galaxy may overcome the degeneracy in M_h. However the STIS data for most nuclei observed with HST are not of sufficient quality to yield best-fit black hole masses.

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