Constraining the Mass Profiles of Stellar Systems: Schwarzschild Modeling of Discrete Velocity Datasets

Abstract

(ABRIDGED) We present a new Schwarzschild orbit-superposition code designed to model discrete datasets composed of velocities of individual kinematic tracers in a dynamical system. This constitutes an extension of previous implementations that can only address continuous data in the form of (the moments of) velocity distributions, thus avoiding potentially important losses of information due to data binning. Furthermore, the code can handle any combination of available velocity components, i.e., only line-of-sight velocities, only proper motions, or a combination of both. It can also handle a combination of discrete and continuous data. The code finds the distribution function (DF, a function of the three integrals of motion E, Lz, and I3) that best reproduces the available kinematic and photometric observations in a given axisymmetric gravitational potential. The fully numerical approach ensures considerable freedom on the form of the DF f(E,Lz,I3). This allows a very general modeling of the orbital structure, thus avoiding restrictive assumptions about the degree of (an)isotropy of the orbits. We describe the implementation of the discrete code and present a series of tests of its performance based on the modeling of simulated datasets generated from a known DF. We find that the discrete Schwarzschild code recovers the original orbital structure, M/L ratios, and inclination of the input datasets to satisfactory accuracy, as quantified by various statistics. The code will be valuable, e.g., for modeling stellar motions in Galactic globular clusters, and those of individual stars, planetary nebulae, or globular clusters in nearby galaxies. This can shed new light on the total mass distributions of these systems, with central black holes and dark matter halos being of particular interest.

ApJ, in press; 51 pages, 11 figures; manuscript revised following comments by referee

References in corpus (4)

• The Kinematics of the Ultra-Faint Milky Way Satellites: Solving the Missing Satellite Problem
• NMAGIC: Fast Parallel Implementation of a Chi-Squared-Made-to-Measure Algorithm for Modelling Observational Data
• Stellar Kinematics in the Complicated Inner Spheroid of M31: Discovery of Substructure Along the Southeastern Minor Axis and its Relationship to the Giant Southern Stream
• Dynamical Models of Elliptical Galaxies in z=0.5 Clusters: I. Data-Model Comparison and Evolution of Galaxy Rotation

Cited by in corpus (2)

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