Axisymmetric Three‐Integral Models for Galaxies

We describe an improved, practical method for constructing galaxy models thatmatch an arbitrary set of observational constraints, without prior assumptionsabout the phase-space distribution function (DF). Our method is an extension ofSchwarzschild's orbit superposition technique. As in Schwarzschild's originalimplementation, we compute a representative library of orbits in a givenpotential. We then project each orbit onto the space of observables, consistingof position on the sky and line-of-sight velocity, while properly taking intoaccount seeing convolution and pixel binning. We find the combination of orbitsthat produces a dynamical model that best fits the observed photometry andkinematics of the galaxy. A key new element of this work is the ability topredict and match to the data the full line-of-sight velocity profile shapes. Adark component (such as a black hole and/or a dark halo) can easily be includedin the models. We have tested our method, by using it to reconstruct the properties of atwo-integral model built with independent software. The test model isreproduced satisfactorily, either with the regular orbits, or with thetwo-integral components. This paper mainly deals with the technical aspects ofthe method, while applications to the galaxies M32 and NGC 4342 are describedelsewhere (van der Marel et al., Cretton & van den Bosch). (abridged)Comment: minor changes, accepted for publication in the Astrophysical Journal Supplement