Session S13: Gravitational Waves: Source Modeling - II

Aligned-spin numerical relativity hybrid surrogate model with subdominant modes.

The era of gravitational wave (GW) astronomy has been emphatically unveiled with the recent detections by LIGO. The mergers of binary black holes (BBHs) were and continue to be one of the most promising sources of GWs. To maximize the science potential of these and future detections, accurate GW models that can reproduce all relevant physical features such as subdominant modes, precession, eccentricity, etc, are crucial. Numerical relativity (NR) simulations provide the most accurate GW waveforms but are prohibitively expensive for applications such as parameter estimation. Surrogate models of NR waveforms have been shown to be both fast and accurate in reproducing the NR waveforms. However, surrogate models constructed until now have only used the NR data, and hence don't span the entire LIGO band for stellar mass binaries. This can be remedied by hybridizing the NR waveforms using post-Newtonian (PN) / effective one body (EOB) waveforms for the early inspiral. We present an aligned-spin surrogate model for hybridized NR-PN/EOB waveforms, that spans the entire LIGO band for stellar mass binaries, includes the effects of subdominant modes and accurately reproduces the hybrid waveforms.   

Development of more fundamental black-hole binary merger waveforms

The discovery of GW150914 and the additional subsequent black-hole binary discoveries made possible by LIGO have been a triumph of theoretical physics as much as experimental physics. Only within the last decade has the state-of-the-art in modeling the final merger waveform in particular become sufficiently accurate to effectively analyze the available data. The advancements within the last decade have been facilitated by the achievements in numerical relativity, and the development of phenomenological models, particularly the ``EOBNR'' and ``IMRPhenom'' families, that can be tuned to available numerical results. While the resulting models provide an effective interpolant for mergers across much of parameter space, they do not provide insight into the underlying dynamics that drive the late inspiral and merger-ringdown waveforms to take the shapes that they do. As a result, these phenomenological approaches may not be sensitive to subtle features in the waveforms, and may not have small enough systematic uncertainties in the era of very loud signals from next-generation ground- and space-based observatories. We will present results of our ongoing effort to address this shortcoming, by developing a method for modeling the final stages of these waveforms that has a stronger foundation in first principles, and avoids the need for tunable degrees of freedom across a subset of parameter space, with clear prospects for extending the methods across a broader range of physical systems.   

Revealing the Final Black Hole from Signal at Maximum Amplitude

Over the last 3 years, we have seen a number of detections of gravitational waves emitted from the coalescence of binary black holes. With the next observational run (O3), we expect more, and potentially louder, detections. One of the desired outcomes of these detections is the ability to perform tests of general relativity using information from the final black hole. One method of finding the parameters of the final black hole is to analyze the ringdown of the signal. Even with the increased sensitivity of the detectors in O3, it will remain difficult to resolve ringdown; however, we will be able to analyze the signal at maximum amplitude. Since this maximum occurs after the black holes have coalesced, we postulate that the parameters of the final black hole can be determined at this point. I discuss a method to determine the state of the final black hole using a relationship between the frequency at maximum amplitude and the quasi-normal mode frequency and decay time of the ringdown. This allows us to take the frequency during the maximum amplitude of the radiation obtained from the detector data and directly relate it to understanding the state of the final black hole.   

SENR/NRPy+: Numerical Relativity in Singular Curvilinear Coordinate Systems

We report on a new open-source, user-friendly numerical relativity code package called SENR/NRPy+. Our code extends previous implementations of the BSSN reference-metric formulation to a broad class of curvilinear coordinate systems, making it ideally-suited for modeling physical configurations with approximate or exact symmetries. It is orders of magnitude more efficient than other widely used, open-source numerical relativity codes when simulating black hole dynamics. The formulation addresses coordinate singularities in the computational domain via cell-centered grids and a simple change of basis that analytically regularizes tensor components with respect to the coordinates. NRPy+ provides a Python-based interface in which equations are written in natural tensorial form and output at arbitrary finite difference order as highly efficient C code, and SENR consolidates the source generated by NRPy+ into an OpenMP-parallelized numerical relativity code. In the context of head-on puncture black hole evolutions, we demonstrate nearly exponential convergence of constraint violation and gravitational waveform errors to zero as the order of spatial finite difference derivatives is increased, while holding the coordinate grids fixed at moderate resolution.   

SENR/NRPy+: Black Hole Binaries on the Desktop

We report on novel techniques designed to enable state-of-the-art black hole binary evolutions from inspiral through ringdown with the SENR/NRPy+ numerical relativity code on consumer-grade desktop computers. These strategies will make possible fully general relativistic gravitational waveform follow-up campaigns at unprecedentedly large scales, as well as the creation of enormous gravitational waveform catalogs with unique systematics.   

Detection and characterization of eccentric compact binary coalescence at the interface of numerical relativity, analytical relativity and machine learning

We present ENIGMA, a time domain, inspiral-merger-ringdown waveform model that describes non-spinning binary black holes systems that evolve on moderately eccentric orbits (https://arxiv.org/abs/1711.06276). The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming moderately eccentric binaries that circularize prior to coalescence, we smoothly match the eccentric inspiral with a stand-alone, quasi-circular merger, which is constructed using machine learning algorithms that are trained with quasi-circular numerical relativity waveforms. We show that ENIGMA reproduces with excellent accuracy the dynamics of quasi-circular compact binaries, and numerical relativity waveforms that describe eccentric binary black hole mergers with mass-ratios $1< q < 5.5$, and eccentricities $e < 0.2$ ten orbits before merger. We use ENIGMA to show that if the gravitational wave events GW150914, GW151226, GW170104 and GW170814 have eccentricities $e\sim0.1$ at 10 Hz, they can be misclassified as quasi-circular binaries due to parameter space degeneracies between eccentricity and spin corrections.   

Toward an analytic model for eccentric waveforms

The emission of gravitational waves causes the eccentricity of binaries to decay, but there are astrophysical scenarios that suggest that some number of binaries may have non-negligible eccentricities when entering the LIGO sensitivity band. This suggests that accurate and efficient waveform models for eccentric binaries may be needed once gravitational wave detectors reach design sensitivity. I will begin by presenting the number of harmonics needed to detect an eccentric signal and to do parameter estimation faithfully. I will then discuss the stationary phase approximation to represent the frequency domain signal. Lastly, we make use of the approximated signal to conduct Markov Chain Monte Carlo parameter estimation studies.   

A Phenomenological Frequency-Domain Waveform Model for Black Hole Kicks

Generic black hole binaries emit gravitational waves anisotropically and carry linear momentum away from the binary in some preferential direction that results in its recoil. Black hole recoils (or kicks) occur largely during the late inspiral and merger phases of evolution and result in Doppler shifted gravitational wave emission. In this talk, I will discuss a new analytic kicked gravitational waveform model that extends existing waveform approximants. This model could be used to measure black hole kicks with future gravitational wave detections.