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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 June 1, 2026
SIEGE: III. The formation of dense stellar clusters in sub-parsec resolution cosmological simulations with individual star feedback
Star clusters stand at the crossroads between galaxies and single stars. Resolving the formation of star clusters in cosmological simulations represents an ambitious and challenging goal, since modelling their internal properties requires very high resolution. This paper is the third of a series within the SImulating the Environment where Globular clusters Emerged (SIEGE) project, where we conduct zoom-in cosmological simulations with sub-parsec resolution that include the feedback of individual stars, aimed to model the formation of star clusters in high-redshift proto-galaxies. We investigate the role of three fundamental quantities in shaping the intrinsic properties of star clusters, i.e., (i) pre-supernova stellar feedback (continuous or instantaneous ejection of mass and energy through stellar winds); (ii) star formation efficiency, defined as the fraction of gas converted into stars per freefall time, for which we test 2 different values (ϵff= 0.1 and 1), and (iii) stellar initial mass function (IMF, standard vs top-heavy). All our simulations are run down toz= 10.5, which is sufficient for investigating some structural properties of the emerging clumps and clusters. Among the analysed quantities, the gas properties are primarily sensitive to the feedback prescriptions. A gentle and continuous feedback from stellar winds originates a complex, filamentary cold gas distribution, opposite to explosive feedback, causing smoother clumps. The prescription for a continuous, low-intensity feedback, along with the adoption of ϵff= 1, also produces star clusters with maximum stellar density values up to 104Mʘpc−2, in good agreement with the surface density-size relation observed in local young star clusters (YSCs). Therefore, a realistic stellar wind description and a high star formation effiency are the key ingredients that allow us to achieve realistic star clusters characterised by properties comparable to those of local YSCs. In contrast, the other models produce too diffuse clusters, in particular the one with a top-heavy IMF.
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- Award ID(s):
- 2009193
- PAR ID:
- 10626414
- Publisher / Repository:
- Astronomy and Astrophysics
- Date Published:
- Journal Name:
- Astronomy & Astrophysics
- Volume:
- 698
- ISSN:
- 0004-6361
- Page Range / eLocation ID:
- A207
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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