Primordial segregation in globular clusters: The degree of mass segregation as determined through dynamical models

¹ Department of Mathematics and Physics, University of Campania Luigi Vanvitelli, viale Lincoln 5, 81100 Caserta, Italy
² INAF – Osservatorio Astronomico d’Abruzzo, Via Mentore Maggini snc, 64100 Teramo, Italy
³ INFN – sezione di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
⁴ Department of Physics, University of Rome La Sapienza, Piazzale Aldo Moro 2, 00185 Rome, Italy
⁵ INFN Sezione di Napoli, Via Cintia snc, 80126 Napoli, Italy

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Received: 29 September 2025
Accepted: 4 February 2026

Abstract

Context. Globular clusters (GCs) are dense stellar systems whose dynamics, which are driven by two-body relaxation, exhibit mass-based processes such as mass segregation and energy equipartition. However, a satisfactory description and quantification of mass segregation is still lacking.

Aims. We characterize the degree of mass segregation through a multi-mass dynamical model that also predicts energy equipartition. Our work focuses on the generation of initial conditions for primordially segregated clusters. We show that these conditions are suitable for N-body simulations of GCs and their multiple populations.

Methods. We quantified the degree of mass segregation by looking at the relation between half-mass radius and stellar mass. We describe how the model inputs change the shape of this function. Furthermore, we developed a customized version of the MCLUSTER code to generate a stellar system based on our dynamical model.

Results. For any degree of mass segregation, the half-mass radius exhibits a linearly decreasing relationship with the stellar mass. Our analysis reveals that the main parameter responsible for the degree of segregation is Φ₀, which represents the strength of the gravitational potential. It is also related to the slope β of the linear approximation. Conversely, the mass function only plays a minor role, where steeper slopes and larger mass ranges result in a slight increase in the degree of segregation. Concerning the generation of stars, our approach successfully provides stellar physical properties, such as density and mean square velocity, and reproduces well the corresponding theoretical profiles. We explore possible realistic initial conditions, such as a Kroupa initial mass function with Φ₀ = 0.01 and 0.1 M_⊙⁻¹, which correspond to a negligible segregation and a highly segregated reference case, respectively. In the context of a two-generation scenario, we can model first-generation stars that exhibit a degree of primordial segregation resulting from violent relaxation. Furthermore, we explore variations in the time elapsed between the formation of the first and the second stellar generations; we consider time intervals of up to 100 Myr, which is a range that is consistent with the asymptotic giant branch self-pollution scenario.

Conclusions. This work further proves the ability of our multi-mass dynamical models to predict mass-based processes, with a focus on mass segregation. This model offers the possibility to set up primordially segregated clusters in a consistent way, and can help us to constrain the poorly understood early phases of GCs and the evolution of their multiple populations.