Made-to-Measure Outperforms Schwarzschild's Method

TL;DR

This paper compares made-to-measure and Schwarzschild's orbit superposition methods in stellar dynamical modeling, finding made-to-measure faster and similarly accurate in reproducing observational data, with some differences in orbit classification.

Contribution

It provides a direct comparison of the two methods' efficiency and accuracy, highlighting the advantages of made-to-measure for galaxy survey analysis.

Findings

Made-to-measure is 3-5 times faster than Schwarzschild's method.

Both methods achieve mean χ² ≈ 1 or less in data reproduction.

Orbit classifications are similar but differ in orbit weights and depend on initial conditions.

Abstract

Syer and Tremaine's made-to-measure method and Schwarzschild's orbit superposition method are well-known within the field of stellar dynamical modeling. This research is concerned with assessing and comparing the operational capabilities of the two methods and, in particular, the impact on observable reproduction, orbit classifications and computer elapsed times when using low orbit numbers (8000 orbits) with different observational data sets and initial conditions. Both methods are able to reproduce observed data with mean $\chi^2 \approx 1$ or less. However, the made-to-measure process does so three to five times faster than the orbit superposition method, and this starts to make the made-to-measure process attractive for analyzing galaxy surveys. For a given set of initial conditions, both methods produce similar orbit classifications but the orbits behind the classifications are not the same. Orbits which are common do not have the same weights. Different initial conditions result in different classifications.