# Made-to-measure modeling of observed galaxy dynamics

## TL;DR

This paper enhances the made-to-measure (M2M) dynamical modeling technique, enabling simultaneous optimization of system parameters and uncertainties, demonstrated through galaxy data and a harmonic oscillator model.

## Contribution

The authors introduce improvements to the M2M method, including simultaneous parameter optimization and a sampling approach for uncertainty quantification in galaxy dynamics modeling.

## Key findings

- Improved M2M method allows joint optimization of nuisance and potential parameters.
- Demonstrated the method with Gaia DR1 data on F-type stars.
- Enabled probabilistic modeling of system uncertainties.

## Abstract

Among dynamical modeling techniques, the made-to-measure (M2M) method for modeling steady-state systems is among the most flexible, allowing non-parametric distribution functions in complex gravitational potentials to be modeled efficiently using N-body particles. Here we propose and test various improvements to the standard M2M method for modeling observed data, illustrated using the simple setup of a one-dimensional harmonic oscillator. We demonstrate that nuisance parameters describing the modeled system's orientation with respect to the observer---e.g., an external galaxy's inclination or the Sun's position in the Milky Way---as well as the parameters of an external gravitational field can be optimized simultaneously with the particle weights. We develop a method for sampling from the high-dimensional uncertainty distribution of the particle weights. We combine this in a Gibbs sampler with samplers for the nuisance and potential parameters to explore the uncertainty distribution of the full set of parameters. We illustrate our M2M improvements by modeling the vertical density and kinematics of F-type stars in Gaia DR1. The novel M2M method proposed here allows full probabilistic modeling of steady-state dynamical systems, allowing uncertainties on the non-parametric distribution function and on nuisance parameters to be taken into account when constraining the dark and baryonic masses of stellar systems.