SIEGE

III. The formation of dense stellar clusters in sub-parsec resolution cosmological simulations with individual star feedback

¹ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
² Lund Observatory, Division of Astrophysics, Department of Physics, Lund University, Box 43, 221 00 Lund, Sweden
³ Department of Astrophysics, American Museum of Natural History, New York, NY 10024, USA
⁴ Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università di Padova, Vicolo dell’Osservatorio 3, 35122 Padova, Italy
⁵ INFN – Padova, Via Marzolo 8, 35131 Padova, Italy
⁶ Institut fuer Theoretische Astrophysik, ZAH, Universitaet Heidelberg, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
⁷ DiSAT, Università degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy
⁸ INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
⁹ Dipartimento di Fisica e Astronomia “Augusto Righi”, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁰ Université Claude Bernard Lyon 1, CRAL UMR5574, ENS de Lyon, CNRS, Villeurbanne 69622, France
¹¹ Department of Astronomy, Indiana University, Bloomington, IN 47401, USA
¹² INAF – Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, 35122 Padova, Italy

^★ Corresponding author.

Received: 4 November 2024
Accepted: 3 March 2025

Abstract

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 (ϵ_ff = 0.1 and 1), and (iii) stellar initial mass function (IMF, standard vs top-heavy). All our simulations are run down to z = 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 ϵ_ff = 1, also produces star clusters with maximum stellar density values up to 10⁴ M_ʘ pc⁻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.