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Abstract
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Abstract

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[*] Velocity profiles of galaxies with claimed black holes - II. f(E,L_z) models for M32
van der Marel R.P., Evans N.W., Rix H.W., White S.D.M., de Zeeuw P.T.
MNRAS, 271, 99-117, 1994
© 1994. The Royal Astronomical Society. All Rights Reserved.

[*] Citations to this paper in the ADS
The galaxy M32 has been claimed to contain a massive central black hole. A major uncertainty in the existing models for M32 is the absence of observational constraints on the dynamical structure and velocity dispersion anisotropy. Here we determine such constraints for the first time. We recently measured kinematical quantities and line-of-sight velocity profile shapes for M32 along five different slit positions (Paper I). We construct axisymmetric dynamical models with distribution functions of the form f(E,L_z) for these data. Such models have sigma_R = sigma_z, and are flattened by an excess of azimuthal motion. We explore two approaches, one based on a set of constant mass-to-light ratio `power law' models recently discussed by Evans, the other based on the moment equations of the collisionless Boltzmann equation. In the latter approach we take into account the central surface brightness cusp observed with HST, and we include a central black hole. We compare the even and the odd part of the observed and predicted velocity profiles separately, and derive independent information on the parts of the distribution function that are even and odd in L_z, respectively.

Models with f(E,L_z) and no central black hole cannot fit the observed central peak in the RMS line-of-sight velocity and the steep central rotation velocity gradient. A good fit to the data in the central arcsec is obtained when M32 is assumed to have a central black hole with mass M_BH = 1.8 x 10^6 solar masses. The major axis rotation velocity of M32 is approximately 90% of that of a maximally streaming f(E,L_z) model. Outside the central arcsec most of the data are remarkably well fitted by the f(E,L_z) models, with two exceptions. First, the even part of the observed major axis velocity profiles is slightly more flat-topped than that predicted by the models. Second, the models predict too much mean streaming on the intermediate axis (major +/- 45 degrees), relative to the major axis. So both the even and the odd part of the distribution function of M32 must in fact depend on a third integral of motion. Our models indicate that M32 most likely has a velocity distribution with [v_phi^2] > [v_theta^2] > [v_r^2] outside the central arcsec.

Our models are more realistic than most previous models in that they take proper account of flattening, rotation and velocity profile data. Yet, the models still require the presence of a massive central black hole. To fit the M32 data without a black hole requires a radially anisotropic velocity distribution in the central region and a tangentially anisotropic velocity distribution in the outer region. The measured excess of azimuthal motion outside the central arcsec is not inconsistent with this picture. However, the required excess of radial motion in the central region may be implausible, given that the central two-body relaxation time in the absence of a central black hole is a factor 10^2 shorter than the Hubble time.

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