Made-to-Measure Modelling of Globular Clusters

TL;DR

This paper introduces a made-to-measure modeling approach for globular clusters, successfully reproducing their properties and providing detailed dynamical insights, including for the specific case of the cluster M4.

Contribution

It is the first application of the made-to-measure method to globular clusters, enabling detailed dynamical modeling and parameter estimation from observational data.

Findings

The method accurately reproduces the density profile of mock clusters.

Partial anisotropy can be recovered with two kinematic properties.

Applied to M4, the model predicts its mass, size, and isotropy.

Abstract

We present the first application of the made-to-measure method for modelling dynamical systems to globular clusters. Through the made-to-measure algorithm, the masses of individual particles within a model cluster are adjusted while the system evolves forward in time via a gravitational $N$-body code until the model cluster is able to reproduce select properties of an observed cluster. The method is first applied to observations of mock isotropic and anisotropic clusters while fitting against the cluster's three dimensional or projected density profile, density weighted mean-squared velocity profile, or its density profile with individual mean-squared velocity profiles. We find that a cluster's three-dimensional density profile can easily be reproduced by the made-to-measure method, with minor discrepancies in the outer regions if fitting against a cluster's projected surface density or projected kinematic properties. If an observed cluster is anisotropic, only fitting against the cluster's density profile and individual mean-squared velocity profiles will fully recover the full degree of anisotropy. Partial anisotropy can be recovered as long as two kinematic properties are included in the fit. We further apply the method to observations of the Galactic globular cluster M4 and generate a complete six-dimensional representation of the cluster that reproduces observations of its surface density profile, mean-squared proper motion velocity profile, and mean-squared line of sight velocity profile. The M2M method predicts M4 is primarily isotropic with a mass of $9.2 \pm 0.4 \times 10^4\, M_{\odot}$ and a half-mass radius of $3.7 \pm 0.1$ pc.