Project results for the general public

The project Growth of black holes in stellar clusters investigated how black holes can form and grow inside dense groups of stars such as globular clusters. These environments contain hundreds of thousands to millions of stars, where close encounters and stellar collisions can sometimes lead to the formation of intermediate-mass black holes. These objects are heavier than ordinary stellar black holes, but lighter than the supermassive black holes found in the centres of galaxies.

A major result of the project was the demonstration that very dense young star clusters can form intermediate-mass black holes through runaway stellar collisions. In this process, repeated collisions between stars in the cluster core can produce a very massive star, which may later collapse into an intermediate-mass black hole. This formation pathway was explored in detail in the Vergara, Askar et al. studies, which used both MOCCA simulations and direct N-body simulations to investigate black hole seed formation in extremely dense stellar systems.

As part of the project, the MOCCA star cluster simulation code was improved and used to simulate a large sample of realistic star clusters. A key part of the work was a detailed comparison between MOCCA Monte Carlo simulations and direct N-body simulations, in particular simulations carried out with NBODY6++GPU. This comparison showed that both approaches predict consistent pathways for runaway stellar collisions and intermediate-mass black hole formation in extremely dense clusters. It also helped guide improvements to the treatment of stellar collisions in MOCCA, especially in models where repeated collisions drive the rapid growth of very massive stars.

Achievements

  • Improved the MOCCA code to better model the formation and evolution of intermediate-mass black holes in dense star clusters.
  • Implemented and tested new prescriptions for stellar collisions, very massive stars, rejuvenation, post-merger evolution and compact-object dynamics.
  • Carried out a large simulation campaign of 268 star cluster models with different initial masses, compactness, metallicities and tidal fields.
  • Published key results showing that intermediate-mass black holes can form through runaway stellar collisions in very dense star clusters.
  • The Vergara, Askar et al. 2025 and 2026 studeis demonstrated that repeated stellar mergers in dense cluster cores can produce very massive stars that may later collapse into intermediate-mass black holes.
  • Compared MOCCA simulations with direct NBODY6++GPU simulations of extremely dense clusters, showing consistent pathways for runaway stellar collisions and black hole seed formation.
  • Used the comparison between MOCCA and direct N-body simulations to improve the treatment of stellar collisions in MOCCA.
  • Developed automated tools to track black hole growth histories, identify important dynamical events and connect simulation data with observable properties of star clusters.
  • Developed post-processing tools to extract photometric and kinematic observables from simulated star cluster models.
  • Extended MOCCA’s computational capabilities toward simulations of extremely massive stellar systems, including models with up to 50 million stars.

Events and scientific activities

  • Project results were presented at international conferences and workshops, including MODEST-24, TMEX-2025, the ACME Workshop, and IAU Symposium 398 / MODEST-25.
  • The PI served as Chair of the Scientific Organizing Committee for the MODEST-24 international conference, hosted at CAMK PAN in August 2024, with more than 130 participants attending in person and online.
  • The PI organized the monthly online seminar series Topics in Star Cluster Evolution & Dynamics (TCE), bringing together researchers from CAMK PAN and international collaborators.
  • The PI co-taught a PhD-level course on Star Cluster Dynamics and Evolution.
  • The PI supervised two Master’s-level students working on project-related topics connected with intermediate-mass black holes and the observable properties of simulated star clusters.

Media presence and public engagement

  • The project was communicated to broader audiences through public talks on astronomy and astrophysics.
  • The PI engaged with school and university students during outreach events and institute open days.
  • Project-related results and publications were shared through open-access articles, arXiv preprints, conference presentations and seminar talks.
  • This section can be updated with links to press releases, interviews, public lectures or media items connected with the project.

Publications and scientific outputs

The project resulted in a highly productive publication output, including peer-reviewed papers, a book chapter and conference proceedings. Selected project-related publications are listed below.

 

Key publications on intermediate-mass black hole formation

  • Rapid formation of a very massive star > 50000 M⊙ and subsequently an IMBH from runaway collisions. Direct N-body and Monte Carlo simulations of dense star clusters
    M. C. Vergara, A. Askar et al., 2025, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202555307
    arXiv: 2505.07491
  • Efficient black hole seed formation in low-metallicity and dense stellar clusters with implications for JWST sources
    M. C. Vergara, A. Askar et al., 2026, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202556878
    arXiv: 2508.14260
  • Formation and growth of intermediate-mass black holes in dense star clusters
    A. Askar, M. C. Vergara, S. Ali, Proceedings of IAU Symposium 398 / MODEST-25
    DOI: 10.48550/arXiv.2510.03766
    arXiv: 2510.03766
  • Intermediate-mass black holes in star clusters and dwarf galaxies
    A. Askar, V. F. Baldassare, M. Mezcua, book chapter in Black Holes in the Era of Gravitational-Wave Astronomy
    DOI: 10.1016/B978-0-32-395636-9.00010-4
    arXiv: 2311.12118

 

Other selected project-related publications

  • Interpretable Machine Learning for Finding Intermediate-mass Black Holes
    Mario Pasquato, Piero Trevisan, Abbas Askar et al., 2024, The Astrophysical Journal
    DOI: 10.3847/1538-4357/ad2261
    arXiv: 2310.18560
  • New Parameters for Star Cluster Dynamics: The Role of Clusters' Initial Conditions
    B. Bhat, B. Lanzoni, E. Vesperini, F. R. Ferraro, F. I. Aros, A. Askar, A. Hypki, 2024, The Astrophysical Journal
    DOI: 10.3847/1538-4357/ad3dec
    arXiv: 2404.06992
  • MOCCA: Global properties of tidally filling and underfilling globular star clusters with multiple stellar populations
    A. Hypki, E. Vesperini, M. Giersz, J. Hong, A. Askar et al., 2025, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202348653
    arXiv: 2406.08059
  • Double white dwarf binary population in MOCCA star clusters: Comparisons with observations of close and wide binaries
    L. Hellström, M. Giersz, A. Hypki, D. Belloni, A. Askar, G. Wiktorowicz, 2024, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202450648
    arXiv: 2405.04314v3
  • Energy equipartition in multiple-population globular clusters
    A. R. Livernois, F. I. Aros, E. Vesperini, A. Askar et al., 2024, Monthly Notices of the Royal Astronomical Society
    DOI: 10.1093/mnras/stae2222
    arXiv: 2410.12968
  • Ultraluminous X-ray sources in Globular Clusters
    G. Wiktorowicz, M. Giersz, A. Askar, A. Hypki, L. Hellström, 2025, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202553723
    arXiv: 2501.06037
  • MOCCA: Effects of pristine gas accretion and cluster migration on globular cluster evolution, global parameters, and multiple stellar populations
    M. Giersz, A. Askar, A. Hypki, J. Hong, G. Wiktorowicz, L. Hellström, 2025, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202452945
    arXiv: 2411.06421
  • Multiple stellar populations in MOCCA globular cluster models: Transient spatial overconcentration of pristine red giant stars driven by strong dynamical encounters
    M. Giersz, A. Askar, A. Hypki, J. Hong, G. Wiktorowicz, L. Hellström, 2025, Astronomy & Astrophysics Letters
    DOI: 10.1051/0004-6361/202554233
    arXiv: 2502.17162
  • Evolution of star clusters with initial bulk rotation via N-body simulations
    A. Bissekenov, X. Pang, A. Kamlah, M. B. N. Kouwenhoven, R. Spurzem, B. Shukirgaliyev, M. Giersz, A. Askar, P. Berczik, 2025, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202554093
    arXiv: 2505.20432
  • Formation channels of gravitationally resolvable double white dwarf binaries inside globular clusters
    L. Hellström, M. Giersz, A. Askar et al., 2025, Astronomy & Astrophysics
    DOI: 10.1051/0004-6361/202555960
    arXiv: 2506.13122
  • Simulations of Globular Cluster Evolution with Multiple Stellar Populations
    M. Giersz, A. Askar, A. Hypki, J. Hong, G. Wiktorowicz, L. Hellström, Proceedings of IAU Symposium 398 / MODEST-25
    DOI: 10.48550/arXiv.2510.06942
    arXiv: 2510.06942

All listed publications are either published in fully open-access journals, made available through journal open-access agreements, or have author-accepted manuscripts freely accessible through open-access repositories such as arXiv.

Open data and datasets

Several datasets connected with the project and related MOCCA/NBODY6++GPU studies are available through open-access repositories.

Funding acknowledgement

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 945339, and from the National Science Centre, Poland, under POLONEZ BIS project no. 2021/43/P/ST9/03167.