The Schwarzschild Method for Building Galaxy Models

Astronomy and Astrophysics – Astronomy

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Scientific paper

Martin Schwarzschild is most widely known as one of the towering figures of the theory of stellar evolution. However, from the early fifties onward he displayed a strong interest in dynamical astronomy, and in particular in its application to the structure of star clusters and galaxies. This resulted in a string of remarkable investigations, including the discovery of what became known as the Spitzer-Schwarzschild mechanism, the invention of the strip count method for mass determinations, the demonstration of the existence of dark matter on large scales, and the study of the nucleus of M31, based on his own Stratoscope II balloon observations. With his retirement approaching he decided to leave the field of stellar evolution, and to make his life--long hobby of stellar dynamics a full-time occupation, and to tackle the problem of self-consistent equilibria for elliptical galaxies, which by then were suspected to have a triaxial shape. Rather than following classical methods, which had trouble already in dealing with axisymmetric systems, he invented a simple numerical technique, which seeks to populate individual stellar orbits in the galaxy potential so as to reproduce the associated model density. This is now known as Schwarzschild's method. He showed by numerical calculation that most stellar orbits in a triaxial potential relevant for elliptical galaxies have two effective integrals of motion in addition to the classical energy integral, and then constructed the first ever self-consistent equilibrium model for a realistic triaxial galaxy. This provided a very strong stimulus to research in the dynamics of flattened galaxies. This talk will review how Schwarzschild's Method is used today, in problems ranging from the existence of equilibrium models as a function of shape, central cusp slope, tumbling rate, and presence of a central point mass, to modeling of individual galaxies to find stellar dynamical evidence for dark matter in extended halos, and/or massive dark objects in galactic nuclei.

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