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

TL;DR

This study addresses why P1 and P2 stellar populations in dynamically-young globular clusters exhibit diverse radial morphologies, including full mixing. It combines analytical theory of binary–single star scattering with direct $N$-body simulations containing massive primordial binaries to quantify heating and redistribution of population P2 relative to P1. The main finding is that binary–single interactions can push centrally formed P2 stars outward and mix the populations within a few relaxation times, with stronger effects in denser clusters and when more or more massive binaries are present; however, radial inversion is not reproduced in the explored setups. The results offer a plausible explanation for fully mixed young GCs like NGC 4590 and NGC 5904 and highlight the role of binary populations in GC evolution, while acknowledging limitations in particle number and the need to explore additional mechanisms (e.g., IMBHs, gas expulsion) in future work.

Abstract

The majority of Galactic globular star clusters (GCs) have been reported to contain at least two populations of stars (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. We aim to investigate the discrepancies between the spatial concentration of P1 and P2 stars in dynamically-young GCs. Our focus is to evaluate whether massive binary stars (e.g. BHs) 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. 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. 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. Binary-single star interactions seem able to explain the observable properties of some dynamically-young GCs (e.g. NGC4590 or NGC5904) where P1 and P2 are fully radially mixed.

Figures (7)

• Figure 1: Estimated semi-major axis (top) and the encounter time scale (bottom) of a binary star that can eject single stars from the core in a cluster of a given mass and half-mass radius. In this plot, we used Eqs. \ref{['eq:abin_alpha']} and \ref{['eq:tenc_alpha']}, for clusters containing stars of equal masses ($m_3=1\,M_\odot$), one binary star with $m_1=m_2=30\,M_\odot$ at its centre, and $v_\infty = 10\,\mathrm{km\,s^{-1}}$. Time in the bottom panel is normalised by the half-mass relaxation time, Eq. \ref{['eq:trh']}.
• Figure 2: Evolution of the half-mass relaxation time, $\tau_\mathrm{rh}(t)$, calculated from Eq. \ref{['eq:trh']} in terms of the initial half-mass relaxation time, $\tau_\mathrm{rh}(0)$. The left-hand set of panels is for the 10k-* clusters, the right-hand set is for 50k-*. The models are separated by the primordial binary star numbers and masses (columns), the binary star initial semi-major axes (colours), and the initial cluster half-mass radius (line styles). Each line is averaged over all realisations of the corresponding model. (We note that the models 10k-5M* and 50k-30M* do not show any differences from the models without binaries, which we also integrated for comparison but do not display them here.)
• Figure 4: The number of massive binaries in each 10k-* model in time (averaged over each model's realisations). The models are separated by their initial $r_\mathrm{h}$ (columns), primordial binary systems (rows), and their semi-major axes (colours). In each plot, the top horizontal axis shows the evolutionary time in the initial half-mass relaxation times, and the lower horizontal axis is in multiples of $\tau_\mathrm{rh}$ at the end of the simulation (to mimic the 'present-day' value). While we permit the dynamical formation of the low-mass ($m_3{+}m_3$) or mixed ($m_{1,2}{+}m_3$) binaries in the simulations, the numbers here only show the massive ($m_1{+}m_2$) binaries, including component switching. However, if the primordial binary goes through a state of an unstable triple, it is not counted towards $N_\mathrm{bin}$ (which is why we sometimes see the number of binaries decreasing and then increasing again).
• Figure 6: The probability density function (PDF) of the binding energy change, $\alpha$, per interaction, in the 10k-* models. Binary--single and binary--binary interactions are counted together. For reference, we also plot with dashed vertical lines the theoretical values of $\alpha$, for which a single $m_3$-star should theoretically escape, as derived using Eq. \ref{['eq:abin_alpha']}. The figure is separated by each model's initial half-mass radius (columns), number and masses of the primordial binaries (rows), and the binary semi-major axes (colours).
• Figure 8: Selected 10k-* models with the highest $A^+$ at $4\,\tau_\mathrm{rh}$ for each primordial binary set-up (as labelled in the top left corners). Top panels: Normalised projected cumulative radial distributions of stars in two populations (P1 and P2 -- distinguished by colours) in the clusters, calculated from Eq. \ref{['eq:Ap']}. All realisations of the corresponding model are plotted. Columns correspond to different values of $R_\mathrm{lim}$. Bottom panels: The ratio of P2 stars in several radial bins leitinger_etal23. Each model realisation is plotted with a black line. The parameter $A^{+}_{R\mathrm{lim}}$ (its maximum range and median with standard deviation) is also displayed for each region.