Physics of eccentric binary black hole mergers: A numerical relativity perspective

Gravitational wave observations of eccentric binary black hole mergers will provide unequivocal evidence for the formation of these systems through dynamical assembly in dense stellar environments. The study of these astrophysically motivated sources is timely in view of electromagnetic observations, consistent with the existence of stellar mass black holes in the globular cluster M22 and in the Galactic center, and the proven detection capabilities of ground-based gravitational wave detectors. In order to get insights into the physics of these objects in the dynamical, strong-field gravity regime, we present a catalog of 89 numerical relativity waveforms that describe binary systems of non-spinning black holes with mass-ratios $1\leq q \leq 10$, and initial eccentricities as high as $e_0=0.18$ fifteen cycles before merger. We use this catalog to quantify the loss of energy and angular momentum through gravitational radiation, and the astrophysical properties of the black hole remnant, including its final mass and spin, and recoil velocity. We discuss the implications of these results for gravitational wave source modeling, and the design of algorithms to search for and identify eccentric binary black hole mergers in realistic detection scenarios.Comment: 11 pages, 5 figures, 2 appendices. A visualization of this numerical relativity waveform catalog is available at https://gravity.ncsa.illinois.edu/products/outreach/; v2: 13 pages, 5 figures, calculations for angular momentum emission and recoil velocities are now included, references added. Accepted to Phys. Rev.

Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers

We present $\texttt{ENIGMA}$, a time domain, inspiral-merger-ringdown waveform model that describes non-spinning binary black holes systems that evolve on moderately eccentric orbits. The inspiral evolution is described using a consistent combination of post-Newtonian theory, self-force and black hole perturbation theory. Assuming 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 $\texttt{ENIGMA}$ reproduces with excellent accuracy the dynamics of quasi-circular compact binaries. We validate $\texttt{ENIGMA}$ using a set of $\texttt{Einstein Toolkit}$ eccentric numerical relativity waveforms, which describe eccentric binary black hole mergers with mass-ratios between $1 \leq q \leq 5.5$, and eccentricities $e_0 \lesssim 0.2$ ten orbits before merger. We use this model to explore in detail the physics that can be extracted with moderately eccentric, non-spinning binary black hole mergers. We use $\texttt{ENIGMA}$ to show that GW150914, GW151226, GW170104, GW170814 and GW170608 can be effectively recovered with spinning, quasi-circular templates if the eccentricity of these events at a gravitational wave frequency of 10Hz satisfies $e_0\leq \{0.175,\, 0.125,\,0.175,\,0.175,\, 0.125\}$, respectively. We show that if these systems have eccentricities $e_0\sim 0.1$ at a gravitational wave frequency of 10Hz, they can be misclassified as quasi-circular binaries due to parameter space degeneracies between eccentricity and spin corrections. Using our catalog of eccentric numerical relativity simulations, we discuss the importance of including higher-order waveform multipoles in gravitational wave searches of eccentric binary black hole mergers.Comment: 19 pages, 10 figures, 1 Appendix. v2: we use numerical relativity simulations to quantify the importance of including higher-order waveform multipoles for the detection of eccentric binary black hole mergers, references added. Accepted to Phys. Rev.

Enabling real-time multi-messenger astrophysics discoveries with deep learning

Multi-messenger astrophysics is a fast-growing, interdisciplinary field that combines data, which vary in volume and speed of data processing, from many different instruments that probe the Universe using different cosmic messengers: electromagnetic waves, cosmic rays, gravitational waves and neutrinos. In this Expert Recommendation, we review the key challenges of real-time observations of gravitational wave sources and their electromagnetic and astroparticle counterparts, and make a number of recommendations to maximize their potential for scientific discovery. These recommendations refer to the design of scalable and computationally efficient machine learning algorithms; the cyber-infrastructure to numerically simulate astrophysical sources, and to process and interpret multi-messenger astrophysics data; the management of gravitational wave detections to trigger real-time alerts for electromagnetic and astroparticle follow-ups; a vision to harness future developments of machine learning and cyber-infrastructure resources to cope with the big-data requirements; and the need to build a community of experts to realize the goals of multi-messenger astrophysics

Solving Master Equations of Continuous-Time, Heterogeneous Agent Uninsurable Income Risk Models Using Deep Learning

As rising wealth inequality is becoming a major component of many present-day economies, the study of dynamic general equilibrium economic models with heterogeneous agents is becoming increasingly important. However, the need for large computational resources due to the “curse of dimensionality” has often made it difficult to solve them using traditional numerical methods such as finite differences. Leveraging recent advances in deep learning, particularly in the physics-informed neural networks (PINNs) literature, we present a novel solution method for solving such models through their master equation formulation. This is done by first approximating the master equation with a large but finite number of agents, transforming it from an infinite-dimensional PDE into a high-dimensional one. We then introduce a PINN algorithm to solve the resulting high-dimensional PDE, whose architecture exploits the symmetry and permutation-invariance properties of the PDE. We show that our algorithm is able to solve with exceptional accuracy the uninsurable income risk model in [2] —a model for which a finite difference solution scheme also exists and serves as a benchmark for comparison. We also provide a preliminary demonstration of our algorithm’s capability to solve models outside the reach of the finite difference method by solving our own proposed uninsurable income risk model where risk aversion is wealth-dependent