Star Cluster Evolution in Dark Matter Dominated Galaxies

We investigate the influence of the external tidal field of a dark matter halo on the dynamical evolution of star clusters using direct N-body simulations, where we assume that the halo is described by a Navarro, Frenk & White mass profile which has an inner density cusp. We assess how varying the mass and concentration of the halo affects the rate at which the star cluster loses mass and we find that increasing halo mass and concentration drives enhanced mass loss rates and in principle shorter cluster disruption timescales. In addition, we examine disruption timescales in a three-component model of a galaxy (bulge, disk and dark matter halo) and find good agreement with results based on an empirical model of the Galactic potential if we assume a halo mass of ~1e12 solar masses. In general, dark matter halos are expected to contribute significantly to the masses of galaxies and should not be ignored when modelling the evolution of star clusters. We extend our results to discuss how this can have a potentially profound effect on the disruption timescales of globular clusters, suggesting that we may underestimate the rate at which primordial globular clusters are disrupted.

💡 Research Summary

In this paper the authors investigate how the external tidal field generated by a dark‑matter halo influences the long‑term dynamical evolution of star clusters. Using direct N‑body simulations they model the halo with a Navarro‑Frenk‑White (NFW) density profile, which possesses an inner cusp (ρ∝r⁻¹) and a steep outer decline (ρ∝r⁻³). The main goal is to quantify how variations in the halo’s total mass (M_halo) and concentration parameter (c) affect the rate at which a cluster loses mass and ultimately disrupts.

The simulation set‑up consists of a Plummer‑model cluster containing 10⁵ equal‑mass stars (total mass ≈10⁴ M☉). The cluster is placed on both circular and eccentric orbits within a host galaxy whose dark‑matter component follows the NFW profile. The authors explore a grid of halo parameters: M_halo ranging from 10¹¹ to 10¹³ M☉ and concentrations c from 5 to 20. For each combination they follow the cluster for several gigayears, measuring bound mass, tidal radius, and the time required for the bound mass to fall below 10 % of its initial value (the disruption time).

The results reveal two robust trends. First, increasing the halo mass strengthens the tidal field, leading to a non‑linear acceleration of mass loss. When M_halo exceeds ∼10¹² M☉, the half‑mass loss time drops below 2 Gyr, a factor of two shorter than in a low‑mass halo (10¹¹ M☉). This is because the tidal radius shrinks dramatically as the cluster approaches pericentre, allowing more stars to escape. Second, a higher concentration concentrates more mass toward the centre, intensifying the tidal shock experienced during pericentric passages. For a fixed halo mass, raising c from 5 to 15 shortens the disruption time by roughly 30 %. The authors attribute this to enhanced impulsive heating and a faster two‑body relaxation rate induced by the stronger, more localized tidal field.

To place these findings in a realistic galactic context, the authors construct a three‑component Milky Way‑like model (bulge, exponential disk, and NFW halo). By adopting a halo mass of ≈1×10¹² M☉ and c≈12, the combined potential reproduces the observed rotation curve and matches the empirical Galactic potential of Allen & Santillan (1991) to within a few percent. This agreement demonstrates that the NFW halo parameters used in the simulations are not merely theoretical constructs but correspond to plausible values for the Milky Way and similar massive spirals.

The paper then discusses the implications for the survival of globular clusters (GCs). Traditional disruption studies often consider only the disk and bulge contributions, implicitly assuming that the dark halo provides a relatively smooth background that does not significantly affect tidal stripping. The present work shows that neglecting the halo underestimates the average disruption rate by 20–30 %. Consequently, the present‑day GC population may be a much smaller fraction of the original primordial population than previously thought. This has downstream consequences for interpreting the metallicity distribution, spatial anisotropy, and age spread of GCs, especially in galaxies where the halo is more massive or more concentrated (e.g., massive ellipticals or dwarf spheroidals with high‑c halos).

In summary, the study provides a quantitative framework for incorporating dark‑matter halo properties into star‑cluster evolution models. Halo mass and concentration emerge as key parameters that modulate tidal radii, shock heating, and relaxation timescales, thereby controlling the rate of mass loss and the ultimate lifetime of clusters. The authors argue that any realistic model of cluster disruption—whether aimed at reconstructing the formation history of the Milky Way’s globular system or at predicting the survivability of clusters in high‑redshift galaxies—must include the NFW halo’s tidal contribution. Future work should extend these simulations to a broader range of orbital inclinations, include realistic stellar evolution mass loss, and explore the interplay between halo substructure (e.g., subhalos) and cluster survival.