Mass modelling globular clusters in the Gaia era: a method comparison using mock data from an $N$-body simulation of M4

TL;DR

This study compares various mass-modelling techniques for globular clusters using mock data from N-body simulations, highlighting their strengths, limitations, and ways to improve accuracy in recovering cluster properties.

Contribution

It provides a comprehensive comparison of distribution-function, Jeans, and N-body models on mock data, identifying their relative accuracies and limitations in globular cluster mass estimation.

Findings

Multimass models outperform single-mass models in accuracy.

Potential escapers affect outer kinematic fits but can be mitigated.

Three-component DF models effectively address mass segregation biases.

Abstract

As we enter a golden age for studies of internal kinematics and dynamics of Galactic globular clusters (GCs), it is timely to assess the performance of modelling techniques in recovering the mass, mass profile, and other dynamical properties of GCs. Here, we compare different mass-modelling techniques (distribution-function (DF)-based models, Jeans models, and a grid of N-body models) by applying them to mock observations from a star-by-star N-body simulation of the GC M 4 by Heggie. The mocks mimic existing and anticipated data for GCs: surface brightness or number density profiles, local stellar mass functions, line-of-sight velocities, and Hubble Space Telescope- and Gaia-like proper motions. We discuss the successes and limitations of the methods. We find that multimass DF-based models, Jeans, and N-body models provide more accurate mass profiles compared to single-mass DF-based models. We highlight complications in fitting the kinematics in the outskirts due to energetically unbound stars associated with the cluster ("potential escapers", not captured by truncated DF models nor by N-body models of clusters in isolation), which can be avoided with DF-based models including potential escapers, or with Jeans models. We discuss ways to account for mass segregation. For example, three-component DF-based models with freedom in their mass function are a simple alternative to avoid the biases of single-mass models (which systematically underestimate the total mass, half-mass radius, and central density), while more realistic multimass DF-based models with freedom in the remnant content represent a promising avenue to infer the total mass and the mass function of remnants.