The Black Hole Tango: Kicks and Spins in Hierarchical Mergers

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Title: Gravitational-Wave Kicks Impact Spins of Black Holes from Hierarchical Mergers
Authors: Angela Borchers, Claire S. Ye, and Maya Fishbach
First Author’s Institution: Max Planck Institute for Gravitational Physics
Status: Published in ApJ

The room is large and densely packed. As you twirl across the floor, someone extends their hand, inviting you to dance. The two of you spin around each other, the tension building with every step. As you draw closer and closer, you realize this isn’t a ballroom, and you’re not people. This is outer space, and you and your partner are black holes, spiraling toward one another in one of the most energetic events in the universe: a black hole merger.

In this cosmic dance, black holes in a binary system orbit each other while also spinning around their own axes. Their spins are inherited from the angular momentum of the massive stars that collapsed to form them. After the two black holes merge, the remnant black hole also spins. The final spin depends on the spins of the two merging black holes and the ratio of the mass of the larger black hole to that of the smaller one. The higher the mass ratio, the more the larger black hole dominates the final spin. To quantify how fast black holes spin, physicists use a dimensionless spin parameter that ranges from 0 (not spinning at all) to 1, the maximum allowed by general relativity.

Observing the distribution of black hole spins helps us understand how binary systems form. For example, binaries formed through isolated channels, where the black holes are born and evolve together, are likely to have similar spin magnitudes, and the directions of their spins tend to align with their orbital motion. In contrast, black holes that form separately and later become a pair through dynamic encounters in dense environments typically have randomly oriented spins (see Figure 1). To determine which formation channels are more common, we need accurate predictions of the expected spin distributions for each scenario to compare them directly to merger observations from detectors like LIGO/Virgo or future gravitational-wave observatories.

In a dense environment, such as a globular cluster, black holes can undergo multiple consecutive mergers, known as hierarchical mergers. With this in mind, we assign “generations” to black holes: first-generation (1G) black holes have never merged, second-generation (2G) black holes are the product of one previous merger, and so on. After several generations, the spin distribution of black holes has been shown to peak at approximately 0.7, independent of the mass ratios and spins of the first-generation binaries. However, studies have often overlooked an important factor that may impact this distribution: recoil kicks.

After a merger, the newly formed black hole receives a “kick” velocity — a shove that sends it moving through space. This happens because gravitational waves carry away linear momentum asymmetrically during the merger, and to conserve momentum, the remnant black hole recoils in the opposite direction. If its kick exceeds the escape velocity of its cluster, the remnant is ejected, making it unlikely to merge again. However, remnants that receive smaller kicks are retained and can go on to merge again, contributing to the spin distribution over multiple generations. The authors of this article study the final spin distribution of black holes that remain within a cluster after forming from hierarchical mergers.

Simulating Binaries in a Globular Cluster

The authors simulate a first-generation population of one million black holes that are assumed to all have the same initial spin, labeled a_i. The authors use data from globular cluster simulations to determine the properties of binaries found in dense environments. The final spin, a_f, and kick velocity of the black holes are calculated using a high-accuracy model of black hole merger remnants. Only black holes with kick velocities less than the escape velocity of typical globular clusters are kept in the population for future mergers. For their analysis across multiple merger generations, the authors test escape velocities of 50, 100, and 200 km/s.

Some initial binary configurations are more likely to produce high kick velocities that could eject the remnant from the cluster. Figure 2 shows that binaries with isotropic (randomly oriented) spins tend to produce larger kicks than those with spins aligned with the orbital motion.

Spin Distribution of 1G + 1G Mergers

Figure 3 shows the final spin distribution from mergers between two first-generation black holes for different initial spin values. It compares all merger remnants (global population) to those that stay in the cluster (retained population). As expected, the distribution peaks around 0.7 for the global population. However, the peak shifts to higher spin values when only retained remnants are considered.

This happens because, as Figure 2 shows, binaries with aligned spins tend to produce lower kick velocities, making them more likely to stay in the cluster. At the same time, aligned spins lead to remnants with higher final spins, so the retained population is biased toward higher spins.

The authors also examine the effect of escape velocity on the spin distribution. Higher escape velocities make the distribution more similar to the global population, while lower escape velocities lead to broader distributions with more support at higher and lower spins.

Spin Distributions of Higher-Generation Mergers

Figure 4 shows how the spin distribution changes over several generations of black hole mergers. As more generations pass, the spin distribution of the retained black holes starts to look quite different from the global one. In particular, it spreads out and shows a broader range of spin values.

The authors also test different starting spin values and escape velocities. While the global spin distribution tends to settle into a consistent shape after a few generations, the authors find that the retained spin distribution does not. Instead, the spin distribution of black holes that stay in the cluster depends on several factors: the binaries’ initial spins and mass ratios, what generation they belong to, and the escape velocity of the cluster. So, there isn’t a single “universal” spin distribution for retained black holes — it changes depending on the environment and merger history.

Hierarchical mergers are considered a pathway to forming intermediate-mass black holes, potentially explaining events like GW190521. Current gravitational-wave detectors are observing more and more black hole mergers, and future detectors will measure their spins more precisely. Accounting for the spin distributions of black holes that remain in clusters rather than the universal distribution will help us better understand and measure how hierarchical mergers contribute to the gravitational-wave population.

Original astrobite edited by Ryan White.

Authored by Viviana Cáceres.