## Appendix## A.1. The JH modelsWe derive here the main properties of the JH models that have been
used in the numerical simulations and in the computations of
and . The reported
quantities are dimensionless, and the normalization constants are
expressed in terms of the total stellar mass ,
the core radius and the gravitational constant
In the hydrodynamical simulations we used the globally isotropic stellar velocity dispersion profile, that we calculate here. For any two-component model the velocity dispersion profile is given by , where is the 1-dimensional radial velocity dispersion. The first term is the isotropic velocity dispersion for the Jaffe model: and the second one describes the contribution due to the Hernquist dark halo: Physically acceptable limits can be easily found for (thus mimicking a black hole at the center of a Jaffe model) and for . The cumulative potential and kinetic energies inside and By integrating over the whole galaxy Eq. (3), we have . The kinetic energy is again the sum of two different contributions, , where and The integration over the whole galaxy of Eq. (4) gives . ## A.2. A centrally flat modelHere we derive the dynamical quantities corresponding to the density distribution The mass contained inside and the potential is The globally isotropic velocity dispersion is given by: As for the JH model, the potential and the kinetic energy inside
the radius and Finally, the projected distribution associated to is: from which one obtains . © European Southern Observatory (ESO) 1998 Online publication: April 20, 1998 |