We model the observed velocity dispersions by solving the Jeans equation for hydrostatic equilibrium. Radial anisotropy (beta = 0.5) is required in the outer parts, to fit the observed velocity dispersion gradient. Near the centre, the data can still be fit equally well with radially anisotropic models without a central black hole, as with less anisotropic models with a central black hole of mass M_BH < 5 x 10^9 solar masses. However, the radially anisotropic Jeans models without a central black hole need not necessarily correspond to a positive and stable distribution function.
We study the central velocity profile of isotropic dynamical models with a central black hole. The wings of the velocity profile are more extended than those of a Gaussian. This is due to the stars that orbit close to the hole at high velocities. The wings contribute significantly to the normalization and the dispersion of the velocity profile. A Gaussian fit to the velocity profile is insensitive to the wings, and thus underestimates both the line strength gamma and the velocity dispersion sigma. In the analysis of real data this effect is even more pronounced, since low frequency information is lost due to continuum subtraction. If M87 has a 5 x 10^9 solar mass black hole, we show that for our observational setup the central line strength will be underestimated by 2% and the central velocity dispersion by 8%. Our blue data shows two puzzling features, seen also in the data of other authors: the central line strength is too small to be accounted for solely by the dilution from non-thermal light, and the velocity dispersion in the centre is 30 km/s smaller than that at R = 0.5 arcsec. The presence of a central black hole can provide a qualitative explanation for both features.
In addition to the stellar kinematics, we determine also the ionized
gas kinematics from the data by analysing the H_gamma emission line.
The central velocity dispersion of the ionized gas is very high at 516
km/s, and drops steeply to 125 km/s at 2 arcsec. Interpretation of the
ionized gas kinematics in terms of a naive isotropic hydrostatic
equilibrium model, implies the presence of a central black hole of
mass M_BH = 3 x 10^9 solar masses.