- [*] Axisymmetric three-integral models for galaxies
- Cretton N., de Zeeuw P.T., van der Marel R.P., Rix H.W.
- ApJ Supplement, 124, 383-401, 1999
- © 1999. The American Astronomical Society.
All Rights Reserved.
this paper in the ADS
We have developed a practical method for constructing galaxy models
that match an arbitrary set of observational constraints, without
prior assumptions about the phase-space distribution function (DF).
Our method is an extension of Schwarzschild's orbit superposition
technique. As in Schwarzschild's original implementation, we compute a
representative library of orbits in a given potential. We then
project each orbit onto the space of observables, consisting of
position on the sky and line-of-sight velocity, while properly taking
into account seeing convolution and pixel binning. We find the
combination of orbits that produces a dynamical model that best fits
the observed photometry and kinematics of the galaxy. A key new
element of this work is the ability to predict and match to the data
the full line-of-sight velocity profile shapes. A dark component (such
as a black hole and/or a dark halo) can easily be included in the
Our method is applicable to any geometry. In an earlier paper (Rix et
al.) we described the basic principles, and implemented them for the
simplest case of spherical geometry. Here we focus on the axisymmetric
case. We first show how to build galaxy models from individual
orbits. This provides a method to build models with fully general DFs,
without the need for analytic integrals of motion. We then discuss a
set of alternative building blocks, the two-integral and the isotropic
components, for which the observable properties can be computed
analytically. Models built entirely from the two-integral components
yield DFs of the form f(E,L_z), which depend only on the energy E and
angular momentum L_z. This provides a new method to construct such
models. The smoothness of the two-integral and isotropic components
also makes them convenient to use in conjunction with the regular
We have tested our method extensively, by using it to reconstruct the
properties of a two-integral model built with independent software.
The test model is reproduced satisfactorily, either with the regular
orbits, or with the two-integral components. Applications of our
method to the galaxies M32 and NGC 4342 are described elsewhere (van
der Marel et al., Cretton & van den Bosch).
Return to my bibliography.
Return to my home page.
Last modified February 4, 1999.
Roeland van der Marel,