SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 333, 433-444 (1998)

Previous Section Next Section Title Page Table of Contents

Appendix

A.1. The JH models

We derive here the main properties of the JH models that have been used in the numerical simulations and in the computations of [FORMULA] and [FORMULA]. The reported quantities are dimensionless, and the normalization constants are expressed in terms of the total stellar mass [FORMULA], the core radius [FORMULA] and the gravitational constant G ; again [FORMULA] and [FORMULA]. The cumulative mass inside [FORMULA] and the total potential are given by:

[EQUATION]

[EQUATION]

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 [FORMULA], where [FORMULA] is the 1-dimensional radial velocity dispersion. The first term is the isotropic velocity dispersion for the Jaffe model:

[EQUATION]

and the second one describes the contribution due to the Hernquist dark halo:

[EQUATION]

[EQUATION]

[EQUATION]

[EQUATION]

Physically acceptable limits can be easily found for [FORMULA] (thus mimicking a black hole at the center of a Jaffe model) and for [FORMULA].

The cumulative potential and kinetic energies inside r can be found analytically for this two-component model, but for simplicity we report here only their total values. The total potential energy is given by [FORMULA], where

[EQUATION]

and

[EQUATION]

By integrating over the whole galaxy Eq. (3), we have [FORMULA]. The kinetic energy is again the sum of two different contributions, [FORMULA], where

[EQUATION]

and

[EQUATION]

The integration over the whole galaxy of Eq. (4) gives [FORMULA].

A.2. A centrally flat model

Here we derive the dynamical quantities corresponding to the density distribution

[EQUATION]

The mass contained inside r is given by

[EQUATION]

and the potential is

[EQUATION]

The globally isotropic velocity dispersion is given by:

[EQUATION]

As for the JH model, the potential and the kinetic energy inside the radius r can be expressed analytically, but here we give only their total values, being the only ingredient required in the definition of [FORMULA]:

[EQUATION]

and

[EQUATION]

Finally, the projected distribution associated to [FORMULA] is:

[EQUATION]

from which one obtains [FORMULA].

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
helpdesk.link@springer.de