Session R17: Gravitational-Wave Modeling

Going Eccentric with Precessing Binaries

Future gravitational wave detectors, especially the Laser Interferometer Space Antenna (LISA), will be sensitive to black hole binaries formed in astrophysical environments that promote large eccentricities and spin precession. Gravitational wave models that include both effects have only recently been developed. One such model, the Efficient Fully Precessing Eccentric (EFPE) model, covers the inspiral stage with small-eccentricity-expanded amplitudes that are accurate for e < 0.3. New approaches are needed to model the inspiral for systems with larger eccentricities. In this work, we develop such a method, improving the leading-order gravitational wave amplitudes of the EFPE model so that they are accurate to e ≤ 0.8. Comparing the new amplitudes to the previous amplitudes in the LISA band, however, reveals that binaries with e₀ ≤ 0.5 at 4 years before merger circularize too quickly for there to be a significant difference between the two models. On the other hand, for e₀ > 0.5, the deviations are significant, particularly for binaries with total masses below 10⁵ solar masses. This suggests that the EFPE model may have a larger regime of validity in eccentricity space than previously thought, making it suitable for inspiral parameter estimation with LISA data, and reinforces the need for moderately eccentric amplitudes to faithfully characterize such binaries.   

Eccentric surrogate waveform model for non-spinning binary black-hole systems

Recently, there has been an increased interest in modeling gravitational waves (GWs) from eccentric binary black hole (BBH) systems, as certain formation channels predict a fraction of detectable binaries could enter the sensitivity band with a measurable eccentricity in future LIGO observing runs (O4 and beyond). Numerical relativity (NR) simulations accurately give the evolution of a binary black-hole (BBH) system and the emitted GW signal. But unfortunately, NR simulations are computationally expensive and cannot be used directly for generating template waveforms for parameter estimation. Surrogate modeling is a data-driven approach that is both fast and accurate in reproducing NR simulations. We present the first 3-dimensional surrogate model for waveforms from eccentric BBH systems that does not require the binary to circularize before merger, with mass ratios from 1 to 4 eccentricity less than 0.4 as measured at a reference time about 20 orbits before merger. Trained directly against 109 NR simulations, these models are shown to reproduce the simulations nearly as accurately as the simulations themselves.   

Surrogate remnant model for non-spinning eccentric binary black hole mergers

The properties of the final remnant (mass, dimensionless spin, and kick velocity) formed at the end of a binary black hole (BBH) coalescence are crucial for fundamental tests of general relativity as well as for astrophysical modeling, including the occurrence of hierarchical mergers. While remnant models for quasi-circular BBH mergers are well-developed, no reliable remnant model is available for eccentric BBH mergers. We perform 109 numerical relativity (NR) simulations featuring non-spinning eccentric BBHs, encompassing mass ratios from 1:1 to 1:4, and eccentricities below 0.4, as measured at a reference time of roughly 20 orbits before merger. These simulations are utilized to construct a data-driven surrogate model for the remnant black hole properties, including final mass, dimensionless spin, and kick velocity. We demonstrate that the remnant model can accurately predict the remnant properties. By leveraging both NR data and the remnant surrogate, we also explore the correlation between the initial eccentricity of the binary and the remnant properties.   

"ESIGMA" - An aligned-spin eccentric IMR waveform model for compact binary mergers

The network of LIGO-Virgo observatories have detected more than a hundred compact binary mergers in their three observing runs. While most binaries tend to circularize when they enter the LIGO-Virgo frequency band, a subpopulation that forms via dynamical interactions in dense stellar clusters can have measurable residual eccentricities. As the size of the gravitational-wave signal catalog grows with increasing detector sensitivity, we are likely to start seeing many of such eccentric merger events. It is therefore timely to develop waveform models that will allow us to accurately characterize and study them. In this talk, we present ESIGMA, an eccentric, aligned-spin, time-domain, inspiral-merger-ringdown (IMR) waveform model for compact binary mergers that includes sub-dominant gravitational-wave harmonics. ESIGMA extends the ENIGMA framework of Huerta et al (2017) by incorporating up-to-date spinning eccentric post-Newtonian results available in literature, and replacing the merger-ringdown prescription with a numerical relativity based surrogate model. We show that ESIGMA has excellent agreement with aligned-spin eccentric numerical relativity simulations. This model will help us understand the astrophysical origins of compact binaries in the ongoing and upcoming observing runs of gravitational wave detectors.   

Extending black-hole remnant surrogate models to extreme mass ratios

Numerical-relativity surrogate models for both black-hole merger waveforms and remnants have emerged as important tools in gravitational-wave astronomy. While producing very accurate predictions, their applicability is limited to the region of the parameter space where numerical-relativity simulations are available and computationally feasible. Notably, this excludes extreme mass ratios. We present a machine-learning approach to extend the validity of existing and future numerical-relativity surrogate models toward the test-particle limit, targeting in particular the mass and spin of post-merger black-hole remnants. Our model is trained on both numerical-relativity simulations at comparable masses and analytical predictions at extreme mass ratios. We extend the gaussian-process-regression model NRSur7dq4Remnant, validate its performance via cross validation, and test its accuracy against additional numerical-relativity runs. Our fit, which we dub NRSur7dq4EmriRemnant, reaches an accuracy that is comparable to or higher than that of existing remnant models while providing robust predictions for arbitrary mass ratios.   

A Ringdown Surrogate Model

The next generation of gravitational-wave detectors will have enough sensitivity to observe hundreds of signals from binary black hole mergers and resolve multiple ringdown frequencies. We will require high-fidelity waveform models to extract as much information as possible from these signals and perform tests of general relativity. In this talk, I will introduce a new, spin-aligned ringdown surrogate model. We use Gaussian process regression, a sophisticated mathematical tool to find joint Gaussian distributions between parameters and data. In future work, this high-precision ringdown surrogate model may be incorporated into a full waveform surrogate.   

Analytical Tests for U(1) Charge in Black Holes Using the Backwards One Body Model

Electric charge is generally neglected when considering astrophysical black holes (BHs), though it is an allowed parameter according to the no hair theorem. Einstein-Maxwell theory, our best current model for combining gravity with electromagnetism, works simply by inserting the electromagnetic stress-energy tensor into Einstein’s equations. Though it is the simplest possible way to couple electromagnetism to gravity, this choice is not unique. Thus, the existence of BHs with non-negligible electric charges would present the opportunity to test Einstein-Maxwell theory. The Backwards One Body (BOB) model has been shown to precisely model the strain for the ringdown, merger, and late inspiral for BH mergers forming Kerr BHs. By extending the BOB model to Kerr-Newman BHs we can perform purely analytical and computationally inexpensive tests for charge from detector signals. In order to demonstrate the validity of BOB within the Kerr-Newman regime, numerical relativity simulations were performed with a modified version of the Einstein Toolkit created by Gabriele Bozzola and Vasileios Paschalidis. Furthermore, this treatment is not unique to electric charge and can be generalized to test for magnetic charges, dark-sector charges, gravitational charges in theories of gravity mediated by a vector field, and any other charges arising from a U(1) symmetry, giving potential opportunities for various tests of fundamental physics.   

First frequency-domain phenomenological model of the multipole asymmetry in gravitational-wave signals from binary-black-hole coalescence

Gravitational-wave signals from binaries that contain spinning black holes in general include an asymmetry between the +m and -m multipoles that is not included in most signal models used in LIGO-Virgo-KAGRA (LVK) analysis to date. This asymmetry manifests itself in out-of-plane recoil of the final black hole and its inclusion in signal models is necessary both to measure this recoil, but also to accurately measure the full spin information of each black hole. We present the first model of the anti-symmetric contribution to the dominant co-precessing-frame signal multipole throughout inspiral, merger and ringdown. We model the anti-symmetric contribution in the frequency domain, and take advantage of the approximations that the anti-symmetric amplitude can be modelled as a ratio of the (already modelled) symmetric amplitude, and analytic relationships between the symmetric and anti-symmetric phases during the inspiral and ringdown. The model is tuned to single-spin numerical-relativity simulations up to mass-ratio 8 and spin magnitudes of 0.8, and has been implemented in a recent phenomenological model for use in the fourth LVK observing run (O4).   

Testing the Boundary to Bound States Dictionary with Numerical Relativity

Recently, the Boundary-to-Bound-states (B2B) dictionary, connecting orbital and radiative observables between bound and unbound orbits, was introduced in the pertubative regime. We produce a large number of numerical simulations of bound and unbound encounters between two non spinning and equal mass black holes in order to test the main results of this dictionary in the non-pertubative regime. We primarily focus on testing the energy and angular momentum radiated, as well as orbital parameters such as the period and periastron advance. We find that, across a wide range of eccentricities, the B2B relationships do not hold in the non-pertubative regime, thus placing a clear limit on the applicability of these relationships for generating gravitational waveforms. Furthermore, we study the boundary between scattering and non scattering encounters and produce an approximate separatrix between these two types of orbits.