Are LIGO's Black Holes Made From Smaller Black Holes? (1703.06869v3)

Abstract: One proposed formation channel for stellar mass black holes (BHs) is through hierarchical mergers of smaller BHs. Repeated mergers between comparable mass BHs leave an imprint on the spin of the resulting BH, since the final BH spin is largely determined by the orbital angular momentum of the binary. We find that for stellar mass BHs forming hierarchically the distribution of spin magnitudes is universal, with a peak at $a \sim 0.7$ and little support below $a \sim 0.5$. We show that the spin distribution is robust against changes to the mass ratio of the merging binaries, the initial spin distribution of the first generation of BHs, and the number of merger generations. While we assume an isotropic distribution of initial spin directions, spins that are preferentially aligned or antialigned do not qualitatively change our results. We also consider a "cluster catastrophe" model for BH formation in which we allow for mergers of arbitrary mass ratios and show that this scenario predicts a unique spin distribution that is similar to the universal distribution derived for major majors. We explore the ability of spin measurements from ground-based gravitational-wave (GW) detectors to constrain hierarchical merger scenarios. We apply a hierarchical Bayesian mixture model to mock GW data and argue that the fraction of BHs that formed through hierarchical mergers will be constrained with $\mathcal{O}(100)$ LIGO binary black hole detections, while with $\mathcal{O}(10)$ detections we could falsify a model in which all component BHs form hierarchically.

Analyzing Stellar Mass Black Holes and Hierarchical Mergers

The paper "Are LIGO's Black Holes Made From Smaller Black Holes?" by Fishbach, Holz, and Farr investigates the potential for stellar mass black holes observed by LIGO to form through hierarchical mergers. Hierarchical merging is a process where smaller black holes, often produced from earlier generations, merge over time to form larger stellar mass black holes. This paper offers significant insights into how initial configurations of merging black holes, such as the mass ratio and spin magnitudes, influence the properties of the resultant black holes.

Key Findings and Methodology:

1. Spin Magnitude Distribution: The authors demonstrate that stellar mass black holes formed hierarchically through major mergers have a universal spin magnitude distribution. This distribution prominently peaks at a dimensionless spin magnitude of approximately $a \sim 0.7$, with scant representation below $a \sim 0.5$. This finding is notable for its robustness across various initial conditions, such as differing mass ratios between merging binaries and varied initial spin orientations.
2. Spin Measurement and Constraints: Utilizing gravitational wave (GW) detections, the paper explores the feasibility of constraining hierarchical merger scenarios. The authors apply a hierarchical Bayesian mixture model to mock LIGO GW data, underscoring that the fraction of black holes forming through hierarchical mergers can be assessed with $\mathcal{O}(100)$ detected binary black hole (BBH) events. Furthermore, the model indicates that using $\mathcal{O}(10)$ detections can falsify scenarios where all component black holes form hierarchically. This approach integrates population-level analysis, surpassing the limits of single-event spin measurements.
3. Cluster Catastrophe Model: The research also considers a model where black holes undergo repeated mergers regardless of mass ratios. This "cluster catastrophe" predicts a unique spin distribution akin to the standard distribution obtained from major mergers, albeit allowing for mergers of arbitrary mass ratios within a cluster environment.
4. Implications and Sensitivity: The paper finds that varying the assumptions regarding the initial spins of black holes or the mass ratios in mergers has marginal effects on the resulting spin distribution, as modeled by the hierarchical mergers. Scenarios allowing aligned or antialigned spins exhibit minimal deviation from the universal distribution, supporting the conclusion that such scenarios invariably result in higher spin magnitudes, typically around $a \sim 0.7$.

Implications and Future Directions:

The implications of this research are manifold. The announced spin magnitude distribution serves as a diagnostic tool to ascertain the nature of stellar mass black holes detected through GWs. Furthermore, as LIGO and other GW observatories increase their detection capabilities, the statistical approach proposed can more finely parse the proportion of black holes that may have formed via hierarchical mechanisms versus those originating from single stellar collapses or other processes.

Theoretically, this framework contributes to our understanding of black hole growth mechanisms, potentially impacting models of stellar evolution, and the dynamics within dense stellar environments, such as globular clusters and galactic nuclei. Practically, advancing the methods for inferring black hole spin distributions and merger histories enriches the serviceability of GW detections as a window into the universe's most enigmatic and energetic processes.

Future research could expand upon this foundation by including sophisticated models of the environments where black hole mergers likely occur, such as accounting for interactions with surrounding gas or nearby stars that could influence spin alignments. Additionally, expanding the mixture models to include more diverse hypothesized spin distributions could refine the technique's discriminatory power between competing astrophysical scenarios. These advancements are crucial for constructing a more holistic picture of black hole formation and growth scenarios in our universe.