[Paper Review] The Dragon-II simulations -- I. Evolution of single and binary compact objects in star clusters with up to 1 million stars

Manuel Arca Sedda, Albrecht Kamlah+8 more|arXiv (Cornell University)|Jul 10, 2023

Astrophysical Phenomena and Observations4 citations

TL;DR

This study presents the Dragon-II simulations, a suite of 19 N-body simulations of star clusters with up to 1 million stars, including up to 33% binary stars, to investigate the dynamical evolution of compact objects (black holes, neutron stars, white dwarfs). The key finding is that black holes form a dense, long-lived subsystem in cluster centers with average masses dropping below 15 M⊙ within 10–30 relaxation times due to BH burning, and that ejected binaries hosting double compact objects have significantly heavier black holes (10–100 M⊙) than those with single compact objects (3–20 M⊙).

ABSTRACT

We present the first results of the extsc{Dragon-II} simulations, a suite of 19 $N$-body simulations of star clusters with up to $10^6$ stars, with up to $33\%$ of them initially paired in binaries. In this work, we describe the main evolution of the clusters and their compact objects (COs). All extsc{Dragon-II} clusters form in their centre a black hole (BH) subsystem with a density $10-100$ times larger than the stellar density, with the cluster core containing $50-80\%$ of the whole BH population. In all models, the BH average mass steeply decreases as a consequence of BH burning, reaching values $\langle m_{ m BH} angle < 15$ M$_\odot$ within $10-30$ relaxation times. Generally, our clusters retain only BHs lighter than $30$ M$_\odot$ over $30$ relaxation times. Looser clusters retain a higher binary fraction, because in such environments binaries are less likely disrupted by dynamical encounters. We find that BH-main sequence star binaries have properties similar to recently observed systems. Double CO binaries (DCOBs) ejected from the cluster exhibit larger mass ratios and heavier primary masses than ejected binaries hosting a single CO (SCOBs). Ejected SCOBs have BH masses $m_{ m BH} = 3-20$ M$_\odot$, definitely lower than those in DCOBs ($m_{ m BH} = 10-100$ M$_\odot$).

Motivation & Objective

• To simulate the dynamical evolution of single and binary compact objects in massive star clusters with up to 1 million stars.
• To investigate how initial cluster properties—such as binary fraction and density—affect the retention and mass evolution of black holes.
• To model the formation, ejection, and properties of black hole-main sequence star and double compact object binaries in dense stellar environments.
• To quantify the impact of dynamical processes like mass segregation and BH burning on the final black hole mass function and spatial distribution.
• To compare simulated compact object populations with observed systems, particularly in globular clusters like NGC3201.

Proposed method

• The simulations employ the Nbody6++GPU code to model star clusters with up to 10^6 stars, including up to 33% initially binary stars.
• Initial conditions are generated using the McLuster code, incorporating realistic stellar initial mass functions and binary parameters.
• Stellar evolution is tracked using a detailed model that includes mass loss, pair-instability and pulsational pair-instability supernovae, and black hole formation with mass gaps.
• Dynamical interactions—such as two-body relaxation, three-body encounters, and binary hardening—are self-consistently evolved over 30 relaxation times.
• Compact object populations are analyzed by tracking mass, spatial distribution, orbital elements, and ejection events from the cluster core.
• The simulations include both single and binary compact objects, with special focus on black hole-main sequence (BH-MS) and double compact object (DCOB) binaries.

Figure 1: Initial density, calculated at the half-mass radius, as a function of number of stars for several grids of direct $N$ -body (blue points) and Monte Carlo (red boxes) simulations. The Dragon-II cluster database is represented by the green star.

Experimental results

Research questions

• RQ1 How do black holes evolve in terms of mass and spatial distribution in dense star clusters over dynamical timescales?
• RQ2 To what extent do dynamical processes such as BH burning and mass segregation alter the initial black hole mass function?
• RQ3 What are the properties of ejected black hole binaries, and how do they compare to observed systems like those in NGC3201?
• RQ4 How does the initial binary fraction influence the retention and evolution of compact object binaries in clusters?
• RQ5 What is the formation efficiency of black holes in the cluster core, and how does it scale with cluster mass and relaxation time?

Key findings

• All Dragon-II clusters form a central black hole subsystem with a density 10–100 times higher than the stellar density, containing 50–80% of the total black hole population within the core radius.
• The average black hole mass decreases steeply due to BH burning, falling below 15 M⊙ within 10–30 relaxation times, regardless of initial cluster properties.
• After 30 relaxation times, clusters retain only black holes with masses below 30 M⊙, indicating strong mass segregation and evaporation of more massive remnants.
• Looser clusters retain a higher binary fraction because dynamical encounters are less likely to disrupt binaries compared to dense clusters.
• Ejected BH–main sequence binaries have lower black hole masses (m_BH < 10 M⊙), shorter orbital periods (<10 days), and are predominantly primordial, unlike those formed in situ.
• Ejected double compact object binaries (DCOBs) have significantly higher primary masses (10–100 M⊙) and larger mass ratios than single compact object binaries (SCOBs), which have m_BH = 3–20 M⊙.

Figure 2: Time evolution of the mass (top panel) and half-mass radius (bottom) of Dragon-II clusters (black lines) compared to observed massive clusters in the Milky Way (MW, blue stars), the two Magellanic Clouds (green squares and red points), the Andromeda galaxy (M31, green squares), the Henize