Triaxial Orbit-based Dynamical Modeling of Galaxies with Supermassive Black Holes and an Application to Massive Elliptical Galaxy NGC 1453

Abstract

Most stellar-dynamical determinations of the masses of nearby supermassive black holes (SMBHs) have been obtained with the orbit superposition technique under the assumption of axisymmetry. However, few galaxies -- in particular massive early-type galaxies -- obey exact axisymmetry. Here we present a revised orbit superposition code and a new approach for dynamically determining the intrinsic shapes and mass parameters of triaxial galaxies based on spatially-resolved stellar kinematic data. The triaxial TriOS code described here corrects a major error in the original van den Bosch et al. (2008) code that gives rise to incorrect projections for most orbits in triaxial models and can significantly impact parameter search results. The revised code also contains significant improvements in orbit sampling, mass constraints, and run time. Furthermore, we introduce two new parameter searching strategies -- a new set of triaxial shape parameters and a novel grid-free sampling technique -- that together lead to a remarkable gain in efficiency in locating the best-fit model. We apply the updated code and search method to NGC~1453, a fast-rotating massive elliptical galaxy. A full 6D parameter search finds \(p=b/a=0.933^{+0.014}_{-0.015}\) and \(q=c/a=0.779\pm0.012\) for the intrinsic axis ratios and \(T=0.33\pm0.06\) for the triaxiality parameter. Despite the deviations from axisymmetry, the best-fit SMBH mass, stellar mass-to-light ratio, and dark matter enclosed mass for NGC~1453 are consistent with the axisymmetric results. More comparisons between axisymmetric and triaxial modeling are needed before drawing general conclusions.