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The mode of star formation that results in the formation of globular clusters and young massive clusters is difficult to constrain through observations. We present models of massive star cluster formation using the TORCHframework, which uses the Astrophysical MUltipurpose Software Environment (AMUSE) to couple distinct multi-physics codes that handle star formation, stellar evolution and dynamics, radiative transfer, and magnetohydrodynamics. We upgraded TORCHby implementing the N-body code PETAR, thereby enabling TORCHto handle massive clusters forming from 106M⊙clouds with ≥105individual stars. We present results from TORCHsimulations of star clusters forming from 104, 105, and 106M⊙turbulent spherical gas clouds (named M4, M5, M6) of radiusR= 11.7 pc. We find that star formation is highly efficient and becomes more so at a higher cloud mass and surface density. For M4, M5, and M6 with initial surface densities 2.325 × 101,2,3M⊙pc−2, after a free-fall time oftff= 6.7,2.1,0.67 Myr, we find that ∼30%, 40%, and 60% of the cloud mass has formed into stars, respectively. The end of simulation-integrated star formation efficiencies for M4, M5, and M6 areϵ⋆ = M⋆/Mcloud = 36%, 65%, and 85%. Observations of nearby clusters similar in mass and size to M4 have instantaneous star formation efficiencies ofϵinst ≤ 30%, which is slightly lower than the integrated star formation efficiency of M4. The M5 and M6 models represent a different regime of cluster formation that is more appropriate for the conditions in starburst galaxies and gas-rich galaxies at high redshift, and that leads to a significantly higher efficiency of star formation. We argue that young massive clusters build up through short efficient bursts of star formation in regions that are sufficiently dense (Σ ≥ 102M⊙pc−2) and massive (Mcloud≥ 105M⊙). In such environments, stellar feedback from winds and radiation is not strong enough to counteract the gravity from gas and stars until a majority of the gas has formed into stars.
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This content will become publicly available on July 1, 2026
SIEGE: IV. Compact star clusters in cosmological simulations with a high star formation efficiency and subparsec resolution
The formation of compact high-redshift star-forming clumps, along with the physical processes driving their evolution and their potential connection to present-day globular clusters (GCs), are key open questions in studies of galaxy formation. In this work, we aim to shed light on these aspects using the SImulating the Environment where Globular clusters Emerged (SIEGE) project, a suite of cosmological zoom-in simulations with subparsec resolution that is specifically designed to investigate the physical conditions behind the origin of compact stellar systems in high-redshift environments. The simulations analyzed in this study are focused on a dwarf galaxy with a virial mass of a few 109M⊙atz= 6.14, where the spatial resolution reaches 0.3 pc h−1. Individual stars are formed directly by sampling the initial mass function, with a 100% star formation efficiency. This setup is designed to explore the impact of a high star formation efficiency under high-redshift conditions. The simulation reveals the emergence of numerous stellar clumps with sizes of 1–3 pc, stellar surface densities up to almost 104M⊙pc−2, and masses predominantly spanning 103M⊙to several 104M⊙, with a few reaching 105M⊙and up to 106M⊙. All clumps form during intense, short bursts of star formation lasting less than a megayear, without noticeable signs of second peaks of star formation or accretion, often with negligible dark matter content (i.e., dark-to-stellar mass ratios below 1 within three times their effective radii). We measured a clear correlation between mass and size, with a clump mass function described by a power law with a slope of −2. Star formation conditions in the simulation reveal a behaviour that is similar to that of a feedback-free starburst scenario, where dense clumps form due to inefficient stellar feedback over small timescales. Notably, some clumps exhibit properties that closely resemble those of present-day globular clusters, highlighting their potential evolutionary connection.
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- Award ID(s):
- 2009193
- PAR ID:
- 10626417
- Publisher / Repository:
- Astronomy and Astrophysics
- Date Published:
- Journal Name:
- Astronomy & Astrophysics
- Volume:
- 699
- ISSN:
- 0004-6361
- Page Range / eLocation ID:
- A31
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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