Post-merger chirps from binary black holes as probes of the final black-hole horizon

The detection of gravitational waves (GWs) has ushered in a new era of astronomy. LIGO and Virgo have detected numerous merging binary black holes (BBHs), binary neutron star mergers, and a potential neutron star-black hole merger. These observations provide insights into compact objects, their populations, and formation channels, while also testing general relativity (GR) in the strong-field regime. However, current detectors lack the sensitivity to observe in detail the merger and relaxation of highly distorted black holes resulting from BBH mergers. Future detectors, like LISA and the Einstein Telescope, will offer unprecedented views of distorted BH horizons, allowing for more detailed tests of GR and exploration of the quantum properties of BHs. Understanding how GW signals encode the source's dynamical properties is crucial for interpreting future high signal-to-noise ratio detections. Current observations reveal a simple 'chirp' morphology with a monotonic increase in frequency and amplitude. However, asymmetric BBHs exhibit more complex morphologies due to strong GW emission in higher-order modes during the merger and ringdown. While the connection between horizon dynamics and GW emission has been studied through correlations between far-field signals and near-horizon fields, and the development of analytical tools, a direct link to GW strain observable by detectors has been missing. This paper aims to establish such a link by correlating an observable feature in the GW strain to a geometrical property of the final BH horizon using numerical relativity simulations.

Previous research has explored the connection between the dynamics of black hole horizons and the gravitational wave emission in two primary ways. The first approach focuses on identifying correlations between far-field gravitational wave signals and the fields near the horizon, revealing links between horizon geometry, gravitational wave flux, and phenomena like the anti-kick. The second approach centers on the development and application of analytical tools designed to probe and interpret the geometrodynamics of spacetime responsible for these correlations. However, these studies largely lack a direct connection to the gravitational wave strain data that detectors can measure. This research builds upon prior works by focusing on finding a direct correlation between a specific observable feature in the gravitational wave strain and the geometry of the final black hole horizon.

Numerical relativity simulations were performed using the MAYA code, based on the Einstein Toolkit. The simulations focused on unequal-mass binary black hole systems. Geometrical units were used, with the total mass of the binary (M) and the speed of light set to unity. The common apparent horizon formation was identified in the simulations. Gravitational wave strain time series and time-frequency maps were generated for observers at various locations around the binary, including face-on, kick-off, kick-on, and an angle approximately 55° from the kick direction. The continuous wavelet transform (using the Morlet wavelet) was applied to analyze the frequency content of the gravitational wave signals. Higher modes of gravitational wave emission were considered. The authors calculated the Newman-Penrose scalar Ψ₄ to represent the gravitational wave emission. The apparent horizon finder (AHFINDERDIRECT) was used to locate and analyze apparent horizons; it was modified to output the 2-metric on the horizon, allowing for the calculation of intrinsic geometric quantities like Gaussian curvature. The gradient of the mean curvature was also calculated. The simulations covered a range of mass ratios (q = m₁/m₂ ≈ 1.1-10). The arc-length parameter was computed along the equator of the apparent horizon to relate the azimuthal angle to the curvature calculations. The authors used the PyCBC and pyCWT software libraries for data analysis.

The simulations revealed multiple post-merger frequency peaks (chirps) near the orbital plane of unequal-mass binaries. These chirps correlate with the line-of-sight passage of regions on the final black hole's dynamical apparent horizon characterized by large mean curvature gradients and locally extremal Gaussian curvature. These regions cluster around a 'cusp'-like defect on the horizon, forming a 'trident' structure. Conversely, frequency minima correlate with the passage of the smoother opposite region of the horizon. The secondary chirp was more intense than the primary chirp for observers at ~55° from the final recoil direction. This double-chirp signature is more pronounced for more asymmetric binaries. A snapshot of the gravitational wave emission in the orbital plane shows distinct wave trains reaching kick-on and kick-off observers with different intensities and time separations. The time delay between the wave trains matches the time delay between frequency peaks in the observed signals, confirming the link between the emission pattern and the observed chirps. The analysis of the near-horizon region reveals an asymmetric pattern in Ψ₄, showing three arms clustering on one side (a 'trident' structure with a cusp) and one arm on the opposite side. This structure rotates and fades as the black hole evolves. Frequency peaks (minima) were observed when these arms (the back) cross the line-of-sight, consistent with the GW travel time. A tight correlation exists between the Ψ₄ maxima (arms) and local maxima of the gradient of mean curvature, with the strongest arm (cusp) precisely matching the maximum of the mean curvature gradient. The Ψ₄ arms also match regions of locally extremal Gaussian curvature. This correlation remains consistent throughout the black hole's evolution, even with some degradation at very late times. The asymmetric structure of the horizon, with the clustering of the three Ψ₄ arms, is maintained during the evolution, spanning an angle of approximately 2.5 radians. Thus, the observed post-merger chirps directly relate to the passage of regions of extremal curvature on the horizon.

The findings demonstrate a direct connection between observable features in post-merger gravitational waves and the geometry of the final black hole's horizon. The observed post-merger chirps are not artifacts of numerical simulations but rather a reflection of the underlying highly distorted geometry of the black hole. The correlation between the chirps and the cusp-like feature on the horizon provides a new tool for probing strong-field gravity and understanding the dynamics of black hole horizons. While the chirps might resemble the signature of black hole echoes, they are associated with standard black holes without exotic features. The fact that these features are more pronounced at approximately 55° from the final kick direction suggests that the orientation of the binary significantly affects the observability of these chirps. Future studies could investigate the influence of black hole spin on this phenomenon.

This research establishes a novel connection between post-merger chirps in gravitational wave signals from binary black hole mergers and specific geometrical features of the final black hole horizon. The discovery of a correlation between multiple frequency peaks in the gravitational waves and the line-of-sight passage of regions with extreme curvature on the horizon opens new avenues for exploring strong-field gravity and testing general relativity. The feasibility of detecting these post-merger chirps with Advanced LIGO at design sensitivity suggests that these observations may be possible before the advent of next-generation detectors. Future work could explore this correlation in more detail, using larger datasets with higher signal-to-noise ratios and potentially incorporating simulations of spinning black holes.

The study focuses on simulations of non-spinning binary black holes. The inclusion of spin effects, which can significantly influence the gravitational wave emission and black hole dynamics, would likely modify the observed correlation. While the authors have addressed gauge dependency, additional simulations with varying numerical parameters could further refine the robustness of the observed results. The late-time degradation of the correlation between the gravitational wave emission and the curvature features may be due to numerical limitations or physical effects not accounted for in the current model.