Several Milky Way star clusters show a roughly flat velocity dispersion profile at large radii, which is not expected from models with a tidal cut-off energy. Possible explanations for this excess velocity include: the effects of a dark matter halo, modified gravity theories and energetically unbound stars inside of clusters. These stars are known as potential escapers (PEs) and can exist indefinitely within clusters which are on circular orbits. Through a series of N-body simulations of star cluster systems, where we vary the galactic potential, orbital eccentricity and stellar mass function, we investigate the properties of the PEs and their effects on the kinematics. We derive a prediction for the scaling of the velocity dispersion at the Jacobi surface due to PEs, as a function of cluster mass, angular velocity of the cluster orbit, and slope of the mass profile of the host galaxy. We see a tentative signal of the mass and orbital velocity dependence in kinematic data of globular clusters from literature. We also find that the fraction of PEs depends sensitively on the galactic mass profile, reaching as high as 40% in the cusp of a Navarro-Frenk-White profile and as the velocity anisotropy also depends on the slope of the galactic mass profile, we conclude that PEs provide an independent way of inferring the properties of the dark matter mass profile at the galactic radius of (globular) clusters in the Gaia-era
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 GCM4 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.
An increasing number of observations of the outer regions of globular clusters (GCs) have shown a flattening of the velocity dispersion profile and an extended surface density profile. Formation scenarios of GCs can lead to different explanations of these peculiarities, therefore the dynamics of stars in the outskirts of GCs are an important tool in tracing back the evolutionary history and formation of star clusters. One possible explanation for these features is that GCs are embedded in dark matter haloes. Alternatively, these features are the result of a population of energetically unbound stars that can be spatially trapped within the cluster, known as potential escapers (PEs). We present a prescription for the contribution of these energetically unbound members to a family of self-consistent, distribution function-based models, which, for brevity, we call the Spherical Potential Escapers Stitched (SPES) models. We show that, when fitting to mock data of bound and unbound stars from an N-body model of a tidally limited star cluster, the SPES models correctly reproduce the density and velocity dispersion profiles up to the Jacobi radius, and they are able to recover the value of the Jacobi radius itself to within 20 per cent. We also provide a comparison to the number density and velocity dispersion profiles of the Galactic cluster 47 Tucanae. Such a case offers a proof of concept that an appropriate modelling of PEs is essential to accurately interpret current and forthcoming Gaia data in the outskirts of GCs, and, in turn, to formulate meaningful present-day constraints for GC formation scenarios in the early Universe.