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.