VELOCITY PROFILES OF GALAXIES WITH CLAIMED BLACK-HOLES .2. F(E, L(Z))MODELS FOR M32

The galaxy M32 has been claimed to contain a massive central black hol e. A major uncertainity in the existing models for M32 is the absence of observational constraints on the dynamical structure and velocity d ispersion anisotropy. Here we determine such constraints for the first time. We recently measured kinematical quantities and line-of-sight v elocity profile shapes for M32 along five different slit positions (Pa per I). We construct axisymmetric dynamical models with distribution f unctions 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 th e latter approach we take into account the central surface brightness cusp observed with the HST, and we include a central black hole. We co mpare the even and the odd parts of the observed and predicted velocit y profiles separately, and derive independent information on the parts of the distribution function that are even and odd in L(z), respectiv ely. Models with f(E, L(z)) and no central black hole cannot fit the o bserved central peak in the rms line-of-sight velocity and the steep c entral rotation velocity gradient. A good fit to the data in the centr al arcsec is obtained when M32 is assumed to have a central black hole with mass M(BH) almost-equal-to 1.8 x 10(6) M(.). The major axis rota tion velocity of M32 is approximately 90 per cent of that of a maximal ly 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 ex ceptions. First, the even parts of the observed major axis velocity pr ofiles are slightly more flat-topped than is predicted by the models. Secondly, the models predict too much mean streaming on the intermedia te axis (major +/- 45-degrees), relative to the major axis. So, both t he even and the odd parts of the distribution function of M32 must in fact depend on a third integral of motion. Our models indicate that M3 2 most likely has a velocity distribution with upsilon(phi)2BAR > upsi lon(theta)2BAR greater-than-or-similar-to upsilon(r)2BAR outside of th e central arcsec. Our models are more realistic than most previous mod els in that they take proper account of flattening, rotation and veloc ity profile data. Yet the models still require the presence of a massi ve central black hole. To fit the M32 data without a black hole requir es a radially anisotropic velocity distribution in the outer region. T he measured excess of azimuthal motion outside the central arcsec is n ot inconsistent with this picture. However, the required excess of rad ial motion in the central region may be implausible, given that the ce ntral two-body relaxation time in the absence of a central black hole is a factor approximately 10(2) shorter than the Hubble time.