Chasing Colliding Black Holes with Stellar Cluster Correlations

Title: A Star Cluster Population of High Mass Black Hole Mergers in Gravitational Wave Data

Authors: Fabio Antonini, Isobel M. Romero-Shaw, Thomas Callister

First Author’s Institution: Gravity Exploration Institute, School of Physics and Astronomy, Cardiff University, Cardiff, CF24 3AA, UK

Status: Accepted to PRL [open access]

Since the first detection of a merging binary black hole in 2015, we have observed around 100 more of these events with gravitational waves (plus more in the currently ongoing observing run). But where do the black holes that we detect come from? One of the biggest clues we have lies in the observable properties of these systems, such as their masses or spins, the two intrinsic properties of a black hole. 

Forming binary black holes

Massive stars tens to hundreds times the mass of our sun form black holes when they die. Bigger stars tend to form bigger black holes, but stellar evolution predicts that stars of certain masses will not form black holes and instead disintegrate at the end of their lives. When these stars die, their extra mass is ejected in pulses of electron-positron pairs due to a (pulsational) pair instability supernova, or (P)PISN. This leaves a mass range where there are predicted to be no black holes that form from stars – this is the so-called (P)PISN mass gap, starting somewhere between 40-70 solar masses and ending at around 130 solar masses. The exact physics of the (P)PISN explosion is subject to a lot of uncertainty, so determining the start of this mass gap is very tricky.

Another confounding factor in determining where this (P)PISN mass gap actually begins comes from the fact that not all of the black holes we detect via gravitational waves form directly from the collapse of massive stars. Stellar clusters are potential factories for black holes with masses in the (P)PISN mass gap. In these environments it’s predicted that there are frequent dynamical interactions between black holes. In particular, two black holes could merge and become an even bigger black hole, and this new descendent could then interact in the cluster and go on to merge again. This is called a hierarchical merger, where the remnant which merged for a second time is called a 2nd generation (2G) black hole, as opposed to a 1st generation (1G) black hole, as shown in figure 1. If two ~35 solar mass black holes merge, they would form a 2G ~70 solar mass black hole. Hence detections of 1G+2G or 2G+2G mergers could populate the (P)PISN mass gap.

Furthermore, black holes formed from binary stars (1G+1G mergers) are thought to have small spins, with their spin vectors similarly aligned to the same direction as the orbital angular momentum. For 2G black holes, simulations based on general relativity predict that their spins will always be ~0.7, where a spin value of 0 is not spinning and 1 is maximally spinning. In hierarchical mergers, because the black holes will meet from any direction in the cluster, their relative angles between spin can be isotropically distributed. At a population level, black holes detected in hierarchical mergers will have a broader distribution of spins and spin tilt angles, while 1G+1G mergers will have a narrower range.

Identifying subpopulations

The authors start with a model where they assume the detected population comes from a mixture of 1G+1G, 1G+2G, and 2G+2G mergers, with some transition mass between the 1G+1G mergers and the hierarchical mergers. The particular value of this transition mass is allowed to vary, and so in comparing the model to the observations, they find the value of this mass which gives the best statistically match to what we detect. They assume that the black holes with masses below the transition mass have small, aligned spins, while the population above this mass can have larger, isotropically distributed spins. Increasing the complexity of their models, they allow the spin distributions of both populations to vary further. With these models, they infer the spin of the 2G black holes, and whether the spin distribution of 1G+1G also changes with mass, to check if their assumptions in the simpler model stand.

For all of the different models the authors implement, they recover a consistent estimate on the transition mass, at ~44 solar masses, despite allowing for this value to be anywhere between 20 and 100 solar masses, as shown on the left panel of figure 2. They find that the data prefers a wider spin distribution at higher masses, meaning that there is strong evidence for hierarchical mergers with a different distribution of spins at higher masses, as shown on the right panel of figure 2. The spin of 2G black holes is also consistent with the ~0.7 prediction from simulations, and there is no evidence that the 1G+1G spin distribution changes with mass below the transition mass. Their results clearly favour two distinct subpopulations in mass and spin which change at ~44 solar masses, implying that this is where the (P)PISN mass gap starts.

Harnessing Correlations

Even though our individual gravitational wave measurements of black hole masses and spins are limited in their precision, this work demonstrates how we can leverage correlations across all of our observations to learn a lot about the underlying astrophysics of black hole formation. Today’s authors find that the hierarchical black hole subpopulation above the (P)PISN mass gap accounts for ~1% of the mergers we detect, but because gravitational wave detections are biased towards detecting certain types of black holes, hierarchical mergers could be ~20% of all merging binary black holes in the universe. With more observations coming in all the time, we should be able to continually improve our understanding of the underlying population of black holes in the universe, helping us to learn about hierarchical mergers, stellar clusters, and black hole astrophysics.

Astrobite edited by Lucas Brown

Featured image credit: ESO/INAF-VST/OmegaCAM. Acknowledgement: A. Grado, L. Limatola/INAF-Capodimonte Observatory, modified by Storm Colloms 

• About the Author

About Storm Colloms

Storm is a postgraduate researcher at the University of Glasgow, Scotland. They work on understanding populations of binary black holes and neutron stars from the gravitational wave signals emitted when they merge, and what that tells us about the lives and deaths of massive stars. Outwith astrophysics they spend their time taking digital and film photos, and making fun doodles of their research.

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