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A central black hole in M32 ?
Roeland P. van der Marel 1 , Hans­Walter Rix 2 , Dave Carter 3 ,
Marijn Franx 4 , Simon D.M. White 5 , Tim de Zeeuw 1
1 Sterrewacht Leiden, Postbus 9513, 2300 RA Leiden, The Netherlands
2 Institute for Advanced Study, Princeton, NJ 8540, USA
3 Royal Greenwich Observatory, Madingley Road, Cambridge CB3 0EZ, England
4 Kapteyn Instituut, Postbus 800, 9700 AV Groningen, The Netherlands
5 Institute of Astronomy, Madingley Road, Cambridge, CB3 0HA, England
ABSTRACT
We have measured the line­of­sight velocity profiles of M32. The major axis velo­
city profiles are asymmetric, with opposite asymmetry on opposite sides of the nucleus.
Existing models for M32 cannot account for these asymmetries. We present new models
which assume the distribution function to be of the form f = f(E; L z ). Such models
require a central black hole of ¸ 1:8 \Theta 10 6 M fi to fit the observed rotation velocities and
velocity dispersions. Without invoking any further free parameters, these models provide
a good fit to the observed velocity profile asymmetries.
1 OBSERVED VELOCITY PROFILES
The presence of a massive black hole has been invoked to match the observed rota­
tion velocities and velocity dispersions at the center of M32 (Tonry 1987; Richstone,
Bower & Dressler 1990). Previous studies have assumed the line­of­sight velocity
distributions of the stars, henceforth referred to as the velocity profiles, to be Gaus­
sian. We have determined the velocity profile shapes of M32 from high S/N spectra
taken with the William Herschel Telescope at La Palma (van der Marel et al. 1993),
using the techniques of Rix & White (1992) and van der Marel & Franx (1993). The
velocity profiles are asymmetric, with the asymmetry changing sign upon going from
one side of the nucleus to the other (see Figure 1). None of the existing models, in
which the local (unprojected) velocity distributions of the stars are assumed to be
Gaussian, can reproduce the observed
asymmetries of the velocity profiles.
Fig. 1---Observed velocity profiles
along the major axis of M32 at galacto­
centric distances of 2 00 , 1 00 , 0 00 , \Gamma1 00 , and
\Gamma2 00 . Note the large velocity dispersion
in the center and the rapid rotation and
significant velocity profile asymmetry
away from the center. The normaliza­
tion is arbitrary.

Fig. 2---
p
V 2 + oe 2 , V , oe,
and the skewness ¸ for the ma­
jor axis of M32. Circles are
estimates for these quantities
obtained from the observed ve­
locity profiles. Results at nega­
tive radii were folded to positive
radii, assuming reflection sym­
metry of the velocity profiles at
opposite radii. The curves show
the seeing convolved predictions
of the two models described in
the text (dashed curves: no
black hole; solid curves MBH =
1:8 \Theta 10 6 M fi ).
2 MODELS
We infer the mass--density profile of M32 from the HST surface photometry
(Lauer et al. 1992), assuming axisymmetry and constant M=L. The distribution func­
tion is assumed to be of the form f(E; L z ) (i.e., oe R = oe z ). Given this, all projected
velocity moments can be calculated from the (higher order) Jeans equations. The only
freedom left is the separation of the second azimuthal velocity moment into streaming
and dispersion. This freedom is used to fit the rotation V and dispersion oe separately,
once the RMS projected line­of­sight velocity
p
V 2 + oe 2 has been calculated.
Figure 2 displays the results for the major axis of M32 (assumed edge­on). A
model without a central black hole cannot fit the observed central peak in
p
V 2 + oe 2 .
However, a good fit is obtained when a central black hole of mass 1:8 \Theta 10 6 M fi is
added. Both models provide an adequate fit to the observed skewness of the line
profile, ¸ j (v \Gamma V ) 3 =oe 3 , without invoking any further free parameters! The black
hole model also fits the data we have for four other slit position angles.
Our modelling does not yet imply that M32 must have a central black hole. To
decide this issue, exploration of the full range of permissible anisotropic models with
three integral distribution functions is required. Work along these lines is in progress.
REFERENCES
Lauer, T.R. et al. 1992, Astr. J., 104, 552.
Richstone, D.O., Bower, G. & Dressler, A. 1990, Ap. J., 353, 118.
Rix, H. & White, S.D.M. 1992, M.N.R.A.S., 254, 389.
Tonry, J.L. 1987, Ap. J., 322, 632.
van der Marel, R.P. & Franx, M. 1993, Ap. J., 407, 525.
van der Marel, R.P., Rix, H., Carter, D., Franx, M., White, S.D.M. & de Zeeuw, P.T.
1993, M.N.R.A.S., submitted.