A novel approach to optimize the regularization and evaluation of dynamical models using a model selection framework

Abstract

ABSTRACT Orbit superposition models are a non-parametric dynamical modelling technique to determine the mass of a galaxy’s central supermassive black hole (SMBH), its stars, or its dark matter halo. One of the main problems is how to decide which model out of a large pool of trial models based on different assumed mass distributions represents the true structure of an observed galaxy best. We show that the traditional approach to judge models solely by their goodness-of-fit can lead to substantial biases in estimated galaxy properties caused by varying model flexibilities. We demonstrate how the flexibility of the models can be estimated using bootstrap iterations and present a model selection framework that removes these biases by taking the variable flexibility into account in the model evaluation. We extend the model selection approach to optimize the degree of regularization directly from the data. Altogether, this leads to a significant improvement of the constraining power of the modelling technique. We show with simulations that one can reconstruct the mass, anisotropy, and viewing angle of an axisymmetric galaxy with a few per cent accuracy from realistic observational data with fully resolved line-of-sight velocity distributions (LOSVDs). In a first application, we reproduce a photometric estimate of the inclination of the disc galaxy NGC 3368 to within 5° accuracy from kinematic data that cover only a few sphere-of-influence radii around the galaxy’s SMBH. This demonstrates the constraining power that can be achieved with orbit models based on fully resolved LOSVDs and a model selection framework.