Gravitational waves from scattering of stellar-mass black holes in galactic nuclei (0807.2638v2)

Abstract: Stellar mass black holes (BHs) are expected to segregate and form a steep density cusp around supermassive black holes (SMBHs) in galactic nuclei. We follow the evolution of a multi-mass system of BHs and stars by numerically integrating the Fokker-Planck energy diffusion equations for a variety of BH mass distributions. We find that the BHs "self-segregate'', and that the rarest, most massive BHs dominate the scattering rate closest to the SMBH (< 0.1 pc). BH--BH binaries form out of gravitational wave emission during BH encounters. We find that the expected rate of BH coalescence events detectable by Advanced LIGO is ~1 - 100/yr, depending on the initial mass function of stars in galactic nuclei and the mass of the most massive BHs. We find that the actual merger rate is likely ~10 times larger than this due to the intrinsic scatter of stellar densities in many different galaxies. The BH binaries that form this way in galactic nuclei have significant eccentricities as they enter the LIGO band (90% with e > 0.9), and are therefore distinguishable from other binaries, which circularise before becoming detectable. We also show that eccentric mergers can be detected to larger distances and greater BH masses than circular mergers, up to ~ 700 solar masses. Future ground-based gravitational wave observatories will be able to constrain both the mass function of BHs and stars in galactic nuclei.

• The paper reveals that stellar-mass black holes self-segregate in galactic nuclei, forming steep density profiles that shape gravitational wave interactions.
• The paper employs numerical simulations and Fokker-Planck integration to model eccentric BH binary formation via gravitational wave capture.
• The paper predicts 1–100 detectable BH merger events per year by Advanced LIGO, highlighting the significance of high eccentricity in merger signals.

Overview of "Gravitational Waves from Scattering of Stellar-Mass Black Holes in Galactic Nuclei"

The paper authored by O'Leary, Kocsis, and Loeb investigates the dynamics and detectability of gravitational wave (GW) signals emanating from scattering events involving stellar-mass black holes (BHs) in galactic nuclei. The work provides a comprehensive analysis of the theoretical framework, numerical simulations, and potential observational implications of such events for upcoming ground-based gravitational wave observatories like Advanced LIGO.

The authors utilize numerical integration of the Fokker-Planck energy diffusion equations to model the formation and evolution of a multi-mass system consisting of BHs and stars around supermassive black holes (SMBHs). One of the critical findings is the self-segregation of BHs, which form a steep density cusp in the vicinity of the SMBH, with the densest regions dominated by the most massive BHs.

Key Findings

1. Black Hole Self-Segregation and Density Profiles: The authors' simulations reveal that BHs exhibit a tendency to self-segregate, forming a steep density profile around SMBHs. The heaviest BHs dominate the vicinity of the SMBH, with implications for the rate and characteristics of BH interactions.
2. Gravitational Wave Capture and Binary Formation: The paper introduces a mechanism through which BH-BH binaries form from gravitational wave emissions during encounters. These binaries, predominantly eccentric, form in the dense environment of a galactic nucleus and have a significantly higher scattering rate compared to binaries that eventually circularize.
3. Merger Rates Detectable by Advanced LIGO: The authors predict that the BH-BH coalescence events detectable by Advanced LIGO are in the range of 1-100 per year. This estimate is dependent on factors such as the initial mass function of stars in galactic nuclei and the mass distribution of the BHs.
4. Eccentricity and Detectability of Mergers: The BH binaries formed in such encounters typically have high eccentricities (90% with $e > 0.9$) when entering the LIGO frequency band, distinguishing them from the more circular inspirals formed from other processes. The paper also notes that eccentric mergers can be detected over larger distances and higher BH masses compared to circular ones, up to a total mass of around 700 solar masses.
5. Implications for Astrophysics and Observations: The work highlights that future gravitational wave observatories could utilize these eccentric merger signals to constrain the mass function of BHs and stars in galactic nuclei. The observations from such detections would advance our understanding of the mass segregation process and the demographic characteristics of black holes in varied astrophysical environments.

Implications and Future Directions

The implications of this research are substantial for both theoretical and observational astrophysics. The formation of eccentric BH binaries as a dominant gravitational wave source challenges current detection strategies that focus primarily on circular inspirals. Introducing eccentricity as an identifiable signature in gravitational wave data could significantly refine our knowledge of BH populations in galactic environments.

The authors also speculate on the utility of such findings for detecting intermediate mass black holes (IMBHs), a topic of immense interest within the field. More research is suggested to explore the influence of additional parameters, such as the role of neutron stars or the potential for resonant relaxation processes altering the distribution of BHs near SMBHs.

In summary, this paper advances the discourse on GW astronomy by providing a framework for detecting and understanding the dynamics of high-eccentricity BH encounters in dense galactic cores. As gravitational wave detection technologies continue to evolve, the kind of detailed predictions made in this paper will be crucial for interpreting the astrophysical signals we observe.