Difficulties with Recovering the Masses of Supermassive Black Holes from Stellar Kinematical Data
Open Access
- 10 February 2004
- journal article
- research article
- Published by American Astronomical Society in The Astrophysical Journal
- Vol. 602 (1), 66-92
- https://doi.org/10.1086/380896
Abstract
We investigate the ability of three-integral, axisymmetric, orbit-based modeling algorithms to recover the parameters defining the gravitational potential (M/L ratio and black hole mass Mh) 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 in most black hole mass determinations to date. A range of parameters (M/L, Mh) can provide equally good fits to the data, making it impossible to assign best-fit values. We illustrate the indeterminacy using a variety of data sets derived from realistic models as well as published observations of the galaxy M32. In the case of M32, our reanalysis demonstrates that data published prior to 2000 are equally consistent with Mh in the range 1.5x10^6-5x10^6 solar masses, with no preferred value in that range. While the HST/STIS data for this galaxy may overcome the degeneracy in Mh, HST data for most galaxies do not resolve the black hole's sphere of influence and in these galaxies the degree of degeneracy allowed by the data may be substantial. We investigate the effect on the degeneracy of enforcing smoothness (regularization) constraints. However we find no indication that the true potential can be recovered simply by enforcing smoothness. For a given smoothing level, all solutions in the minimum-chisquare valley exhibit similar levels of noise. These experiments affirm that the indeterminacy is real and not an artifact associated with non-smooth solutions. (Abridged)Comment: Accepted for publication in The Astrophysical Journal. Changes include discussion of regularizatioKeywords
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This publication has 58 references indexed in Scilit:
- Why (inner) bars are important but not sufficientProceedings of the International Astronomical Union, 2004
- The Counterrotating Core and the Black Hole Mass of IC 1459The Astrophysical Journal, 2002
- Evidence for a Supermassive Black Hole in the S0 Galaxy NGC 3245The Astrophysical Journal, 2001
- Evidence of a Supermassive Black Hole in the Galaxy NGC 1023 from the Nuclear Stellar DynamicsThe Astrophysical Journal, 2001
- Axisymmetric Three‐Integral Models for GalaxiesThe Astrophysical Journal Supplement Series, 1999
- Evidence for a Massive Black Hole in the S0 Galaxy NGC 4342The Astrophysical Journal, 1999
- Improved Evidence for a 3 × 10[TSUP]6[/TSUP] [ITAL]M[/ITAL][TINF]⊙[/TINF] Black Hole in M32: Canada-France-Hawaii Telescope Spectroscopy with FWHM = 0[farcs]47 ResolutionThe Astrophysical Journal, 1996
- Modelling galaxies with Formula: a black hole in M32Monthly Notices of the Royal Astronomical Society, 1995
- Velocity mapping and models of the elliptical galaxies NGC 720, NGC 1052, and NGC 4697The Astrophysical Journal, 1990
- Stellar dynamics and the description of stellar systemsPhysics Reports, 1986