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Peer-reviewedCC BYMonthly Notices of the Royal Astronomical Society

FROST-CLUSTERS – III. Metallicity-dependent intermediate-mass black hole formation by runaway collisions in dense star clusters

  • Antti Rantala1,2,3
  • Thorsten Naab3
  • Natalia Lahén3,4
  • Klaus Reuter5
  • Markus Rampp5
  • Martyna Chruślińska6
  • B. Reinoso7
7 affiliations
  1. 1Institute of Astronomy, University of Cambridge , Madingley Road, Cambridge CB3 0HA ,
  2. 2Kavli Institute for Cosmology, Cambridge (KICC), University of Cambridge , Madingley Road, Cambridge CB3 0HA ,
  3. 3Max-Planck-Institut für Astrophysik , Karl-Schwarzschild-Str 1, D-85748 Garching ,
  4. 4Zentrum für Astronomie der Universität Heidelberg, Astronomisches Rechen-Institut , Mönchhofstr 12-14, D-69120 Heidelberg ,
  5. 5Max Planck Computing and Data Facility (MPCDF) , D-85748 Garching ,
  6. 6European Southern Observatory , Karl-Schwarzschild-Str 2, D-85748 Garching ,
  7. 7University of Helsinki Department of Physics, , PO Box 64, Gustaf Hällströmin katu 2, FI-00014 Helsinki ,
Open at sourceDOICite

Abstract

We explore the formation of intermediate-mass black holes (IMBHs), potential seeds for supermassive black holes (SMBHs), via runaway stellar collisions for a wide range of star cluster (surface) densities (4× 103 ≲ Σ h ≲ 4× 106 M⊙ pc−2) and metallicities (0.01 ≲ Z ≲ 1.0 Z⊙ ). Our sample of isolated (>1400) and hierarchical (30) simulations of young, massive star clusters with up to N=1.8× 106 stars includes collisional stellar dynamics, stellar evolution, and post-Newtonian equations of motion for black holes using the bifrost code. High stellar wind rates suppress IMBH formation at high metallicities (Z ≳ 0.2 Z⊙), and low collision rates prevent their formation at low densities (Σ h≲ 3× 104 M⊙ pc−2). The assumptions about stellar wind loss rates strongly affect the maximum final IMBH masses (M• ∼ 6000 M⊙ versus M• ∼ 25 000 M⊙). The total stellar mass loss from collisions and collisionally boosted winds before t=3 Myr can together reach up to 5–10 per cent of the final cluster mass. We present fitting formulae for IMBH masses as a function of host star cluster Σ h and Z which can be used to seed SMBHs in high-resolution cosmological hydrodynamical simulations and in semi-analytic models for galaxy formation. Our results favour IMBH formation in dense low-metallicity environments similar to z∼ 10 JWST (James Webb Space Telescope) proto-globular clusters. IMBH formation is suppressed in the high-metallicity and low-density conditions of the local Universe.

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Cite

BibTeXRIS
BibTeX
@article{rantala2026frostclusters,
  title = {{FROST-CLUSTERS – III. Metallicity-dependent intermediate-mass black hole formation by runaway collisions in dense star clusters}},
  author = {Antti Rantala and Thorsten Naab and Natalia Lahén and Klaus Reuter and Markus Rampp and Martyna Chruślińska and B. Reinoso},
  journal = {Monthly Notices of the Royal Astronomical Society},
  year = {2026},
  month = may,
  doi = {10.1093/mnras/stag986},
  url = {https://doi.org/10.1093/mnras/stag986},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - FROST-CLUSTERS – III. Metallicity-dependent intermediate-mass black hole formation by runaway collisions in dense star clusters
AU  - Antti Rantala
AU  - Thorsten Naab
AU  - Natalia Lahén
AU  - Klaus Reuter
AU  - Markus Rampp
AU  - Martyna Chruślińska
AU  - B. Reinoso
PY  - 2026
DA  - 2026/05/27
JO  - Monthly Notices of the Royal Astronomical Society
DO  - 10.1093/mnras/stag986
UR  - https://doi.org/10.1093/mnras/stag986
AB  - We explore the formation of intermediate-mass black holes (IMBHs), potential seeds for supermassive black holes (SMBHs), via runaway stellar collisions for a wide range of star cluster (surface) densities (4× 10^3 ≲ Σ _h ≲ 4× 10^6 M_⊙ pc^−2) and metallicities (0.01 ≲ Z ≲ 1.0 Z_⊙ ). Our sample of isolated (>1400) and hierarchical (30) simulations of young, massive star clusters with up to N=1.8× 10^6 stars includes collisional stellar dynamics, stellar evolution, and post-Newtonian equations of motion for black holes using the bifrost code. High stellar wind rates suppress IMBH formation at high metallicities (Z ≳ 0.2 Z_⊙), and low collision rates prevent their formation at low densities (Σ _h≲ 3× 10^4 M_⊙ pc^−2). The assumptions about stellar wind loss rates strongly affect the maximum final IMBH masses (M_• ∼ 6000 M_⊙ versus M_• ∼ 25 000 M_⊙). The total stellar mass loss from collisions and collisionally boosted winds before t=3 Myr can together reach up to 5–10 per cent of the final cluster mass. We present fitting formulae for IMBH masses as a function of host star cluster Σ _h and Z which can be used to seed SMBHs in high-resolution cosmological hydrodynamical simulations and in semi-analytic models for galaxy formation. Our results favour IMBH formation in dense low-metallicity environments similar to z∼ 10 JWST (James Webb Space Telescope) proto-globular clusters. IMBH formation is suppressed in the high-metallicity and low-density conditions of the local Universe.
SN  - 0035-8711
SN  - 1365-2966
SN  - 1365-8711
ER  -