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