Monte Carlo cluster simulations by Cabrera & Rodriguez (2023) showed that binary–single encounters involving compact objects (black holes or neutron stars) in globular-cluster cores can eject stars at more than 2000 km/s, beyond the star-only speed limit of Leonard (1991), and that the velocity distribution of such ejecta is skewed toward lower speeds than the observed hypervelocity-star (HVS) population, complementing Galactic-center Hills-mechanism ejections that are skewed toward higher speeds. Two linked questions remain open: (1) a first-principles derivation of the maximum ejection velocity attainable in binary–single encounters with compact objects — the compact-object analogue of Leonard's star-only limit — including its scaling with compact-object mass, binary hardness, and encounter geometry, with the physical cutoffs (tidal disruption, physical collision, or relativistic capture) that replace stellar surface escape speed as the ceiling; and (2) a self-consistent Milky Way population model that simultaneously includes globular-cluster compact-object ejections and Galactic-center Hills ejections, treats their strongly time-dependent relative rates with realistic cluster-formation history and Galactic potential, and tests whether the combined picture quantitatively reproduces the kinematic and spatial properties of observed high-velocity stars. No derivation of the compact-object speed limit and no construction of the combined model exist in the literature through 2026; the closest follow-up (Evans et al. 2025) models the globular-cluster channel alone.

Background

Hypervelocity stars (HVSs) are stars moving faster than the local escape speed of the Galaxy, and runaway stars are their slower counterparts that remain gravitationally bound; both classes require powerful acceleration mechanisms beyond ordinary supernova or two-body relaxation kicks. The classical origin, proposed by Hills (1988), is the Hills mechanism: a stellar binary passing close to the supermassive black hole at the Galactic center is tidally disrupted, and one component is ejected at up to several thousand km/s while the other remains bound. For strong three- or four-body encounters among ordinary stars in clusters, Leonard (1991) established by numerical scattering experiments a star-only speed limit: the maximum ejection speed is approximately the surface escape speed of the most massive star involved (about 620 km/s for a Sun-like star), because a stellar participant cannot survive a close passage that would impart more energy than this.

Globular clusters (GCs) are dense, ancient stellar systems whose cores host frequent strong gravitational encounters, including binary–single scattering in which a single object undergoes a close resonant or flyby interaction with a binary; when at least one participant is a compact object (a black hole or neutron star, produced by stellar collapse), the encounter is a BSCO (binary–single compact object) encounter. Because compact objects are far more compact than stars, the physical closeness an encounter can reach — and hence the binding energy that can be transferred to an ejected body — is much larger. Cabrera & Rodriguez (2023) used Monte Carlo N-body cluster models (cluster-evolution codes that sample stellar encounters statistically rather than integrating every star, coupled with direct few-body integration of each strong encounter) matched to the observed Milky Way GC population and found that BSCO encounters eject stars at more than 2000 km/s, exceeding Leonard's star-only limit, though contributing only about 1.5–20% of runaways and at most about 1% of HVSs.

Two gaps follow from their results. First, on the dynamics side, there is no first-principles (analytic) theory of the maximum ejection velocity for encounters involving compact objects: Leonard's limit does not apply because its physical ingredient — stellar surface escape speed — is replaced by tidal disruption of any stellar companion, physical collision, or relativistic capture, so the ceiling and its scaling with compact-object mass, binary hardness (binding energy, set by masses and semi-major axis), and encounter geometry must be re-derived. The existing analytic theory of the velocity distribution of the Hills channel (Rossi, Kobayashi & Sari 2014) treats the supermassive-black-hole binary-disruption problem, not comparable-mass compact-object encounters. Second, on the population side, single-channel models are in tension with data: Galactic-center origin studies find HVS velocity distributions skewed toward higher speeds than observed (Brown et al. 2018), while Generozov & Perets (2022) showed that a Galactic-center model including star-formation history cannot reproduce the observed deficiency of stars above about 700 km/s, and Cabrera & Rodriguez (2023) found the GC compact-object channel skewed toward speeds below about 500 km/s. This motivates a combined population-synthesis model of both channels, weighted by their relative rates — which evolve strongly over cosmic time, from a few 10% of the overall runaway rate in the first few Gyr to a few percent today — propagated through a realistic Galactic potential, and tested against the kinematic and spatial distribution of the observed HVS sample. Related single-channel groundwork exists: escape mechanisms from GCs generally (Weatherford et al. 2023), Hills-like ejections from clusters hosting intermediate-mass black holes (Fragione & Gualandris 2019), and observational back-integration classification of extreme-velocity star origins (Li et al. 2023), but none combines the two channels.

Problem Statement

The problem is to complete the quantitative characterization of high-speed stellar ejections produced by binary–single encounters involving compact objects in globular clusters, as posed by Cabrera & Rodriguez (2023), in two linked parts that jointly answer one question: what is the dynamical reach and the population-level contribution of this channel to the Galaxy's high-velocity stars, and can it combined with the Galactic-center Hills mechanism reproduce the observed population?

(1) Compact-object speed limit. Derive from first principles the maximum ejection velocity attainable when a single star encounters a binary containing at least one black hole or neutron star — the compact-object analogue of Leonard's (1991) star-only limit, capturing how the ceiling depends on compact-object mass, binary hardness (component masses and semi-major axis), mass ratios, and encounter geometry. Because the Newtonian point-mass problem alone admits no finite maximum, the derivation must identify the physical cutoffs (tidal disruption of any stellar companion, physical collision, or relativistic capture at the hardest stable post-encounter binary) that make the ceiling finite. The relevant encounters span both the resonant channel (in which the intruding star is temporarily captured and undergoes chaotic interchange with the binary) and the flyby exchange channel (in which the binary is perturbed without temporary capture), over the parameter space of neutron-star and black-hole binaries with stellar companions at cluster-core encounter velocities.

(2) Combined population model. Construct a self-consistent Milky Way population-synthesis model that simultaneously includes ejections from globular-cluster binary–single compact-object encounters and Hills-mechanism ejections from the Galactic center, coupled to their relative ejection rates — which evolve, following the globular-cluster formation history, from a few 10% of the overall runaway rate in the first few Gyr to a few percent at the present day — and to propagation through a realistic Galactic potential. Use the model to apportion the relative contributions of the two channels and to test whether the combined picture quantitatively reproduces the velocity and spatial distributions of the observed high-velocity and hypervelocity star sample.

Part (1) characterizes the kinematic reach of the globular-cluster compact-object channel and part (2) its population-level contribution; together they address whether globular-cluster compact-object encounters are a dynamically significant contributor to the observed hypervelocity-star population.

References

  1. Cabrera, T., & Rodriguez, C. L. 2023, 'Runaway and Hypervelocity Stars from Compact Object Encounters in Globular Clusters', The Astrophysical Journal 953, 19, DOI 10.3847/1538-4357/acdc22, arXiv:2302.03048, https://arxiv.org/abs/2302.03048
  2. Leonard, P. J. T. 1991, 'The maximum possible velocity of dynamically ejected runaway stars', The Astronomical Journal 101, 562, DOI 10.1086/115704, https://doi.org/10.1086/115704
  3. Hills, J. G. 1988, 'Hyper-velocity and tidal stars from binaries disrupted by a massive Galactic black hole', Nature 331, 687, DOI 10.1038/331687a0, https://doi.org/10.1038/331687a0
  4. Brown, W. R., Lattanzi, M. G., Kenyon, S. J., & Geller, M. J. 2018, 'Gaia and the Galactic Center Origin of Hypervelocity Stars', The Astrophysical Journal 866, 39, DOI 10.3847/1538-4357/aadb8e, https://doi.org/10.3847/1538-4357/aadb8e
  5. Generozov, A., & Perets, H. B. 2022, 'Constraints on the origins of hypervelocity stars: velocity distribution, mergers, and star formation history', Monthly Notices of the Royal Astronomical Society 513, 4257, DOI 10.1093/mnras/stac1108, arXiv:2112.13864, https://arxiv.org/abs/2112.13864
  6. Evans, F. A., Grondin, S. M., Ye, C. S., Webb, J., Laroche, A., & Bovy, J. 2025, 'The ejection and detectability of high- and hyper-velocity stars by compact object binaries in globular clusters', arXiv preprint (submitted to ApJ), arXiv:2506.14273, https://arxiv.org/abs/2506.14273
  7. Fragione, G., & Gualandris, A. 2019, 'Hypervelocity stars from star clusters hosting intermediate-mass black holes', Monthly Notices of the Royal Astronomical Society 489, 4543, DOI 10.1093/mnras/stz2451, arXiv:1808.07878, https://arxiv.org/abs/1808.07878
  8. Rossi, E. M., Kobayashi, S., & Sari, R. 2014, 'The Velocity Distribution of Hypervelocity Stars', The Astrophysical Journal 795, 125, DOI 10.1088/0004-637X/795/2/125, arXiv:1307.1134, https://arxiv.org/abs/1307.1134
  9. Li, Q.-Z., Huang, Y., Dong, X.-B., Zhang, H.-W., Beers, T. C., & Yuan, Z. 2023, 'On the Origins of Extreme Velocity Stars as Revealed by Large-scale Galactic Surveys', The Astronomical Journal 166, 12, DOI 10.3847/1538-3881/acd1dc, arXiv:2207.04406, https://arxiv.org/abs/2207.04406
  10. Weatherford, N. C., Kıroğlu, F., Fragione, G., Chatterjee, S., Kremer, K., & Rasio, F. A. 2023, 'Stellar Escape from Globular Clusters. I. Escape Mechanisms and Properties at Ejection', The Astrophysical Journal 946, 104, DOI 10.3847/1538-4357/acbcc1, arXiv:2211.16523, https://arxiv.org/abs/2211.16523