SIEGE

IV. Compact star clusters in cosmological simulations with a high star formation efficiency and subparsec resolution

¹ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Gobetti 93/3, 40129 Bologna, Italy
² Department of Astronomy, Indiana University, Bloomington, Swain West, 727 E. 3rd Street, IN 47405, USA
³ Centre de Recherche Astrophysique de Lyon UMR5574, Univ Lyon, Univ Lyon1, Ens de Lyon, CNRS, 69230 Saint-Genis-Laval, France
⁴ Dipartimento di Fisica e Astronomia ‘Augusto Righi’, Università di Bologna, via Piero Gobetti 93/2, 40129 Bologna, Italy
⁵ Physics and Astronomy Department Galileo Galilei, University of Padova, Vicolo dell’Osservatorio 3, 35122, Padova, Italy
⁶ INFN – Padova, Via Marzolo 8, 35131 Padova, Italy
⁷ Institut für Theoretische Astrophysik, ZAH, Universität Heidelberg, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
⁸ Como Lake Center for Astrophysics (CLAP), DiSAT, Università degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy

^★ Corresponding author: raffaele.pascale@inaf.it

Received: 2 December 2024
Accepted: 6 May 2025

Abstract

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 10⁹ M_⊙ at z = 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 10⁴ M_⊙ pc⁻², and masses predominantly spanning 10³ M_⊙ to several 10⁴ M_⊙, with a few reaching 10⁵ M_⊙ and up to 10⁶ M_⊙. 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.