[Paper Review] Runaway Collisions in Star Clusters

Simon Portegies Zwart, Junichiro Makino+2 more|arXiv (Cornell University)|Dec 11, 2000

Stellar, planetary, and galactic studies3 citations

TL;DR

This study uses high-precision N-body simulations with stellar and binary evolution to demonstrate that runaway stellar collisions are common in dense, young star clusters like R136, the Arches, and the Quintuplet. The collision rate scales linearly with inverse initial relaxation time, reaching ~2.2×10⁻⁴ collisions per star per Myr in clusters with a 1 Myr relaxation time, indicating that such collisions significantly alter cluster evolution even in modest-sized systems.

ABSTRACT

We study the occurrence of physical collisions between stars in young and compact star cluster. The calculations are performed on the GRAPE-4 with the starlab software environment which include the dynamical evolution and the nuclear evolution of all stars and binaries. The selection of the initial conditions is based on existing and well observed star clusters, such as R136 in the 30 Doradus region in the Large Magellanic Cloud and the Arches and Quintuplet star clusters in the vicinity of the Galactic center. Collisions between stars occurred rather frequently in our models. At any time a single star dominates the collision history of the system. The collision rate of this runaway merger scales with the initial relaxation time of the cluster and is independent on other cluster parameters, such as the initial mass function or the initial density profile of the cluster. Subsequent encounters result in a steady grow in mass of the coagulating star, until it escapes or explodes in a supernova. The collision rate in these models is about 0.00022 collisions per star per Myr for a cluster with an initial relaxation time of 1 Myr.

Motivation & Objective

• To investigate whether physical stellar collisions occur frequently in dense, young star clusters such as R136, the Arches, and the Quintuplet.
• To determine whether runaway collision processes can dominate cluster evolution, even in systems with relatively low initial relaxation times.
• To assess the impact of stellar collisions on the dynamical and evolutionary evolution of star clusters, including the formation of massive stars and black holes.
• To challenge prior assumptions that collisions are rare and negligible in cluster evolution by using direct N-body simulations with full stellar and binary evolution.
• To quantify the collision rate and its dependence on cluster parameters such as relaxation time, mass function, and density profile.

Proposed method

• N-body simulations using the Starlab software environment with the GRAPE-4 special-purpose computer for high-speed integration.
• Incorporation of self-consistent stellar and binary evolution (via SeBa) and dynamical feedback between stellar evolution and cluster dynamics.
• Initial conditions based on observed clusters: R136, Arches, and Quintuplet, with varied numbers of stars (1k to 32k), relaxation times, and initial mass functions.
• Use of the relaxation time as the primary scaling parameter for collision rates, with models run under varying initial density profiles (Heggie-Ramamani models with W₀ = 1 to 7).
• Inclusion of Galactic tidal fields and treatment of supernova explosions with variable mass loss to assess ejection and black hole formation.
• Analysis of collision histories, mass growth of central objects, and cluster expansion due to mass loss from supernovae.

Experimental results

Research questions

• RQ1 What is the actual rate of physical stellar collisions in dense, young star clusters with realistic initial conditions?
• RQ2 Does a single star undergo runaway collisions, and if so, what determines the rate of such collisions?
• RQ3 How does the collision rate depend on cluster parameters such as relaxation time, initial mass function, and density profile?
• RQ4 To what extent do stellar collisions alter the dynamical evolution of the cluster, including core expansion and eventual dissolution?
• RQ5 What happens to the remnants of collision-born massive stars, particularly whether they form black holes that continue to grow via further collisions?

Key findings

• The collision rate per star per million years scales as $ \mathcal{R}_{\rm coll} = 2.2 \times 10^{-4} \, t_{\rm rlx}^{-1.0} \, [\text{Myr}^{-1}] $, with $ t_{\rm rlx} $ in Myr, indicating a strong dependence on initial relaxation time.
• A single star dominates the collision history in each cluster, growing in mass through repeated collisions until it either explodes as a supernova or is ejected.
• Runaway collisions occur even in clusters with fewer than $ 10^7 $ stars, contradicting earlier assumptions that such systems require very large masses.
• The massive product of multiple collisions is well separated in mass from other stars, making it potentially observable as a very massive star or black hole.
• Supernova explosions of the collision-born star may eject it from the cluster if significant mass is lost, but if mass loss is minimal, the resulting black hole can remain in the core and continue growing via further collisions.
• Core expansion due to mass loss from supernovae eventually terminates the collision efficiency, limiting the duration of runaway collision phases to a few 10 Myr.