A new type of compact stellar population: dark star clusters

Among the most explored directions in the study of dense stellar systems is the investigation of the effects of the retention of supernova remnants, especially that of the massive stellar remnant black holes (BHs), in star clusters. By virtue of their eventual high central concentration, these stellar mass BHs potentially invoke a wide variety of physical phenomena, the most important ones being emission of gravitational waves (GWs), formation of X-ray binaries, and modification of the dynamical evolution of the cluster. Here we propose, for the first time, that rapid removal of stars from the outer parts of a cluster by the strong tidal field in the inner region of our Galaxy can unveil its BH sub-cluster, which appears as a star cluster that is gravitationally bound by an invisible mass. We study the formation and properties of such systems through direct N-body computations and estimate that they can be present in significant numbers in the inner region of the Milky Way. We call such objects “dark star clusters” (DSCs) as they appear dimmer than normal star clusters of similar mass and they comprise a predicted, new class of entities. The finding of DSCs will robustly cross-check BH retention; they will not only constrain the uncertain natal kicks of BHs, thereby the widely debated theoretical models of BH formation, but will also pinpoint star clusters as potential sites for GW emission for forthcoming ground-based detectors such as the Advanced LIGO. Finally, we also discuss the relevance of DSCs for the nature of IRS 13E.

💡 Research Summary

The paper investigates a previously unrecognized class of stellar systems that the authors term “dark star clusters” (DSCs). The central idea is that in the strong tidal field of the inner Milky Way (within a few kiloparsecs of the Galactic centre), the outer layers of a star cluster can be stripped away on a timescale shorter than the self‑depletion time of a centrally concentrated sub‑cluster of massive stellar remnants (black holes, and to a lesser extent neutron stars). When the luminous stars are largely removed, the remaining dark remnants dominate the gravitational potential. Consequently, the surviving luminous stars appear super‑virial (virial coefficient Q* > 1) and the system would be interpreted observationally as a star cluster with an anomalously high mass‑to‑light ratio – a “dark” cluster bound by invisible mass.

To test this scenario the authors performed direct N‑body simulations with NBODY6, including realistic stellar evolution (Hurley et al. 2000) and GPU acceleration. Initial conditions were Plummer models with total masses between 10⁴ and 7.5 × 10⁴ M⊙, half‑mass radii 1–3.5 pc, and a Kroupa IMF (α = −1.3 for 0.07–0.5 M⊙, α = −2.3 above 0.5 M⊙). All supernova remnants were assumed to receive low natal kicks so that they remain bound at birth. The clusters orbit a point‑mass bulge of 2 × 10¹⁰ M⊙ on circular trajectories.

The simulations reveal that black holes (≈10 M⊙) and neutron stars (≈2 M⊙) quickly mass‑segregate to the centre, forming a Spitzer‑unstable sub‑system. As the external tidal field removes low‑mass stars from the outskirts, the luminous component’s kinetic energy increasingly exceeds the self‑gravitating equilibrium, driving Q* well above the canonical 0.5. While the total system remains bound (Q < 1), the observable stars become effectively unbound, producing the DSC signature.

Key quantitative results include:

• For a cluster with M₀ = 3 × 10⁴ M⊙, r_h₀ = 3.5 pc at R_G = 2 kpc, the DSC phase (Q* > 1) lasts ≈150 Myr; a more relaxed criterion (Q* > 0.75) extends the phase to ≈250 Myr.
• The DSC lifetime increases with galactocentric distance because tidal stripping weakens, but beyond ≈5.5 kpc the time required to reach the DSC state exceeds the age of the Galaxy, making DSC formation unlikely there.
• Assuming a constant cluster formation rate of 0.16 M⊙ yr⁻¹ in the inner 10 kpc and a Schechter initial‑cluster mass function, the authors estimate ≈75 DSCs with Q* > 1 and ≈125 with Q* > 0.75 currently residing within 5 kpc of the centre.

The paper also applies the DSC concept to the enigmatic IRS 13E complex near Sgr A*. Earlier interpretations invoked an intermediate‑mass black hole (~1300 M⊙) to bind a handful of massive young stars, but recent proper‑motion studies have ruled out such a massive single object. The authors therefore explore whether a dense sub‑cluster of stellar‑mass black holes could provide the required invisible mass. Using a pre‑evolved (3.5 Myr) Plummer model with a top‑heavy IMF (α ≈ 0, lower mass cutoff ≈35 M⊙) and total N ≈ 6500, they find that after rapid tidal stripping the system collapses to a half‑mass radius of ≈0.02 pc, containing ≈130 black holes (total ≈1300 M⊙) and fewer than ten luminous O‑type stars. At this stage the luminous component is highly super‑virial (Q* ≫ 1), matching the DSC definition and reproducing the observed compactness and stellar content of IRS 13E. Although this scenario requires an extreme IMF and initial conditions, it demonstrates that a DSC could plausibly explain the dynamics of IRS 13E without invoking an intermediate‑mass black hole.

The authors discuss several broader implications. First, the existence of DSCs would provide a direct observational test of black‑hole natal kick distributions and retention fractions in dense clusters. Second, the dense black‑hole cores of DSCs are fertile sites for black‑hole binary formation and hardening, making DSCs promising progenitors of gravitational‑wave events detectable by Advanced LIGO/Virgo and future space‑based detectors such as LISA. Third, the high mass‑to‑light ratios of DSCs could be identified in upcoming astrometric surveys (e.g., GAIA) and high‑resolution infrared observations of the Galactic centre. Finally, the study highlights the importance of coupling realistic stellar evolution, dynamical mass segregation, and external tidal fields to predict novel observable phenomena in the Milky Way’s inner regions.

In summary, Banerjee and Kroupa present a compelling theoretical framework for a new class of compact stellar systems—dark star clusters—formed by tidal stripping of ordinary stars and the survival of a centrally concentrated black‑hole sub‑cluster. Their direct N‑body experiments predict that dozens of such objects should exist within the inner few kiloparsecs of the Milky Way, and that at least one known object (IRS 13E) may already be an example. Detection of DSCs would simultaneously constrain black‑hole formation physics, enrich our understanding of Galactic dynamics, and identify new laboratories for gravitational‑wave astrophysics.