Biases in the determination of dynamical parameters of star clusters: today and in the Gaia era

TL;DR

This study assesses biases in deriving star cluster properties using analytic models versus N-body simulations, highlighting current limitations and future improvements with Gaia data.

Contribution

It identifies key biases in mass, mass function, and anisotropy estimates and proposes methods to reduce uncertainties, emphasizing Gaia's potential for enhanced accuracy.

Findings

Mass estimates can vary by up to 50% depending on cluster relaxation and observational factors.

Mass function slope is more reliably constrained unless clusters are highly evolved.

Current models poorly reproduce anisotropy characteristics, detectable only with precise proper motions.

Abstract

The structural and dynamical properties of star clusters are generally derived by means of the comparison between steady-state analytic models and the available observables. With the aim of studying the biases of this approach, we fitted different analytic models to simulated observations obtained from a suite of direct N-body simulations of star clusters in different stages of their evolution and under different levels of tidal stress to derive mass, mass function and degree of anisotropy. We find that masses can be under/over-estimated up to 50% depending on the degree of relaxation reached by the cluster, the available range of observed masses and distances of radial velocity measures from the cluster center and the strength of the tidal field. The mass function slope appears to be better constrainable and less sensitive to model inadequacies unless strongly dynamically evolved clusters and a non-optimal location of the measured luminosity function are considered. The degree and the characteristics of the anisotropy developed in the N-body simulations are not adequately reproduced by popular analytic models and can be detected only if accurate proper motions are available. We show how to reduce the uncertainties in the mass, mass-function and anisotropy estimation and provide predictions for the improvements expected when Gaia proper motions will be available in the near future.