Black Hole Dynamics in Stellar Clusters

Abstract

Star clusters can harbour many exotic objects, including black holes (BHs), X-ray binaries and blue straggler stars. In dense stellar environments like globular clusters (GCs), two-body relaxation drives their dynamical evolution, where gravitational interactions between stars strive to equalize their kinetic energy in the cluster. Theoretical studies have indicated that some of these clusters can retain a substantial number of stellar-mass black holes. As these black holes are more massive than typical stars, they segregate to the cluster centre due to dynamical friction and can form a black hole subsystem (BHS). In the last decade, several BH candidates have been observed in GCs.

In crowded cores of GCs, frequent gravitational encounters between stars and binary systems can occur. The exchange of energy in these interactions help sustain the cluster's core from collapsing. Abundant interactions among BHs can lead to their coalescence under the emission of gravitational waves to create intermediate-mass BHs (IMBHs) with masses of a few hundred to thousands of times the mass of our Sun. This project sheds light on how the presence of a BHS or an IMBH can influence the evolution and present-day observable properties of GCs.

We utilize results from over 1500 GC models that were simulated using the MOCCA code for evolving realistic star clusters. We correlate the clusters' dynamical state to the distributions and observable signatures of various stellar populations. Using the simulation output, we investigate cluster morphologies, retention rates of BHs and the distributions of observable stellar populations in the absence or presence of BHs or IMBHs. We quantify the segregation between stellar populations using the Dr50 and A+ parameters, which measure their relative distributions from the centre of the cluster. These parameters are used to quantify the difference in cumulative radial distributions between populations of main-sequence stars, blue stragglers and giants. We find that segregation is more enhanced in clusters with short relaxation times that are likely to be hosting an IMBH. Formation rates of blue stragglers are equally related to the cluster's relaxation time. An increased number of blue stragglers are found in heavily segregated (A+ > 0.05) clusters with relaxation times (~1 Gyr) having significant central surface brightness. Longer relaxation times and large half-mass radii are associated with clusters forming a BHS, with central surface brightness < 10^{4} L⊙ pc^{-2}.

Clusters hosting IMBHs with large initial binary fractions (95%) have a retained median binary fraction of ≈ 12% in the innermost 0.05 parsecs that decreases in a power-law ~(r/rhl)^{-0.132} outwards, while BHS models have a slightly increased binary fraction in their cores of ≈ 14% with a shallower slope of ~(r/rhl)^{-0.013}. For clusters with initial binary fractions of 10%, core binary fractions are still higher for BHS models, but have a faster depletion outwards compared to models hosting an IMBH. We conclude that clusters with initially short relaxation times are typically heavily segregated and contain IMBHs with fewer, but harder, binaries in their cores, contrary to systems with many BHs. Since clusters neither hosting a BHS nor an IMBH might also have short relaxation times and strong segregation, low binary fractions and large central surface brightness values can become a further indication for the presence of an IMBH.

Using segregation values for 50 known GCs in the Milky way, we predict numbers of BHs and masses of IMBHs by correlating the simulated numbers and masses of BHs with observed segregation. Comparable estimates with recently published works are produced, in particular, for NGC 3201, where we find an estimate of 64^{+158}_{-45} BHs retained in the cluster. We also note that 47 Tuc is best explained hosting an IMBH in our parameter space. We stress that the dynamics of BHs affect segregation on a more substantial grade than initial concentration and that short relaxation times and extensive segregation can be sufficient enough for ruling out the presence of a BHS, but further information about core binary fractions and central surface brightness is needed to identify clusters harbouring an IMBH.

Popular Abstract

Since the beginning of time, humankind has been fascinated by the night sky illuminated by distant stars. Even with the naked eye, one can see that stars are often grouped together in clusters. These dense environments can be the birthplace of many mysterious and exotic astrophysical objects in our Universe.

Star clusters are collections of stars born at the same time and are bound together by the influence of gravity. This attractive force acts over long distances and affects everything with energy or mass. In less crowded locations like our solar neighbourhood, stars are unlikely to gravitationally interact with each other. However, in more dense environments, like star clusters, where hundreds to millions of stars can be packed in very small volumes, stars can gravitationally interact. These gravitational encounters drive the dynamical evolution of dense star clusters. Early in the life of a star cluster, its most massive stars (that could be up to a few tens of the mass of our Sun) evolve first and end their lives to form black holes; these are objects so compact that not even light can escape their gravitational pull. This project sheds light on how the presence of black holes in star clusters can influence their long-term evolution and affect the observable properties of the cluster and its constituent stars.

In dense environments like star clusters, massive objects experience friction against the background of abundant lower mass stars and rapidly sink to the cluster's centre. In these dense centres, frequent gravitational encounters between stars allow them to exchange energy. These interactions can also result in collisions, where exotic stars can form due to the coalescence of multiple stellar objects. Since black holes are the most massive objects in a cluster, they will sink to the centre first and can interact to form systems of multiple black holes. If these are numerous enough, they can form a subsystem of black holes. Dynamical interactions between black holes can lead to the formation of binary systems containing two black holes on tight orbits around their common centre of mass. These can coalesce under the influence of gravity and the emission of gravitational waves. The latter produces ripples in space-time which have been observed by the LIGO/VIRGO ground-based gravitational wave detectors. In the densest star clusters, mergers between black holes can lead to the formation of an intermediate-mass black hole (IMBH) which is hundreds to thousands of times the mass of the Sun.

This project aims at finding differences in observable signatures of simulated star clusters depending on if the centre of the cluster hosts either a subsystem of black holes or an intermediate-mass black hole. Comparable to stars generating radiative energy through nuclear reactions in their cores, black holes in the core of a cluster exchange energy with lighter components that prevent the cluster from collapsing under its own gravity. If black holes are numerous, they energise bright components on wider orbits and increase the cluster's brightness in the outskirts. Conversely, their absence allows luminous stars to migrate to the cluster's centre. Thus, observational properties of clusters varies depending on their central objects.

We use computer simulations of hundreds of star cluster models with different initial sizes and densities to look for signatures of the presence of black holes or IMBHs. Since stars distribute differently under their influence, we can find the difference between the distributions of heavy as opposed to lighter stars and measure how segregated a cluster is.
We investigate how these differences depend on the number of black holes in the clusters. We find that systems hosting IMBHs have a higher fraction of brighter stars in their cores. The presence of an IMBH also depletes the number of binaries in the cluster centre. By investigating the relationship between the number of black holes retained and the mass of these more massive black holes depending on their segregation, we predict the numbers and masses of black holes in observed clusters. Seeing that our current techniques still limit direct observations of black holes, these simulations can help resolve the signatures for the presence of some of the most exotic objects in the Universe.

• author: Strickert, Markus
• supervisor: Abbas Askar
• organization: Department of Astronomy and Theoretical Physics - Undergoing reorganization; Lund Observatory - Undergoing reorganization
• course: ASTM32 20221
• year: 2022
• type: H2 - Master's Degree (Two Years)
• subject: Physics and Astronomy
• keywords: Black Holes, Globular Clusters, Dynamics, Intermediate-mass black holes, Simulations
• language: English
• id: 9095211
• date added to LUP: 2022-07-11 09:06:43
• date last changed: 2022-07-11 09:06:43