Spatial mixing of stellar populations in globular clusters via binary–single star scattering

¹ Astronomical Institute of the Czech Academy of Sciences, Boční II 1401, 141 00 Prague 4, Czech Republic
² Department of Astronomy, Indiana University, Swain Hall West, 727 E 3 rd Street, Bloomington, IN 47405, USA
³ Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden
⁴ Dipartimento di Fisica e Astronomia, Università degli Studi di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
⁵ European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany
⁶ School of Mathematics and Physics, The University of Queensland, St. Lucia, QLD 4072, Australia
⁷ School of Physics and Astronomy, Monash University, Clayton, Victoria 3800, Australia
⁸ ARC Centre of Excellence for Gravitational Wave Discovery – OzGrav, Australia
⁹ Technion – Israel Institute of Technology, Physics Department, Haifa 32000, Israel
¹⁰ Vyoma GmbH, Karl-Theodor-Straße 55, 80803 Munich, Germany
¹¹ Max-Planck Institute for Astronomy (MPIA), Königstuhl 17, 69117 Heidelberg, Germany
¹² Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 06300 Nice, France
¹³ Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, London E1 4NS, UK

^★ Corresponding author: pavlik@asu.cas.cz

Received: 5 August 2025
Accepted: 7 October 2025

Abstract

Context. The majority of Galactic globular star clusters (GCs) have been reported to contain at least two populations of stars (hereafter, we use P1 for the primordial and P2 for the chemically enriched population). Recent observational studies found that dynamically old GCs have P1 and P2 spatially mixed due to relaxation processes. However, in dynamically young GCs, where P2 is expected to be more centrally concentrated from birth, the spatial distributions of P1 and P2 are sometimes very different from system to system. This suggests that more complex dynamical processes specific to certain GCs might have shaped those distributions.

Aims. We aim to investigate the discrepancies between the spatial concentration of P1 and P2 stars in dynamically young GCs. Our main focus is to evaluate whether massive binary stars (e.g. black holes) can cause the expansion of the P2 stars through binary–single interactions in the core, and whether they can mix or even radially invert the P1 and P2 distributions.

Methods. We use a set of theoretical and empirical arguments to evaluate the effectiveness of binary–single star scattering. We then construct a set of direct N-body models with massive primordial binaries to verify our estimates further and gain more insights into the dynamical processes in GCs.

Results. We find that binary–single star scatterings can push the central P2 stars outwards within a few relaxation times. While we do not produce radial inversion of P1 and P2 for any initial conditions we tested, this mechanism systematically produces clusters where P1 and P2 look fully mixed even in projection. The mixing is enhanced (1) in denser GCs, (2) in GCs containing more binary stars, and (3) when the mass ratio between the binary components and the cluster members is higher.

Conclusions. Binary–single star interactions seem able to explain the observable properties of some dynamically young GCs (e.g. NGC 4590 or NGC 5904) where P1 and P2 are fully radially mixed.