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Abstract Standardizing the definition of eccentricity is necessary for unambiguous inference of the orbital eccentricity of compact binaries from gravitational wave observations. In previous works, we proposed a definition of eccentricity for systems without spin-precession that relies solely on the gravitational waveform, is applicable to any waveform model, and has the correct Newtonian limit. In this work, we extend this definition to spin-precessing systems. This simple yet effective extension relies on first transforming the waveform from the inertial frame to the coprecessing frame, and then adopting an amplitude and a phase with reduced spin-induced effects. Our method includes a robust procedure for filtering out spin-induced modulations, which become non-negligible in the small eccentricity and large spin-precession regime. Finally, we apply our method to a set of Numerical Relativity and Effective One Body waveforms to showcase its robustness for generic eccentric spin-precessing binaries. We make our method public via Python implementation ingw_eccentricity. 

Abstract The Simulating eXtreme Spacetimes Collaboration's code \texttt{SpEC} can now routinely simulate binary black hole mergers undergoing $$\sim25$$ orbits, with the longest simulations undergoing nearly $$\sim180$$ orbits. While this sounds impressive, the mismatch between the highest resolutions for this long simulation is $$\mathcal{O}(10^{-1})$$. Meanwhile, the mismatch between resolutions for the more typical simulations tends to be $$\mathcal{O}(10^{-4})$$, despite the resolutions being similar to the long simulations'. In this note, we explain why mismatch alone gives an incomplete picture of code---and waveform---quality, especially in the context of providing waveform templates for LISA and 3G detectors, which require templates with $$\mathcal{O}(10^{3}) - \mathcal{O}(10^{5})$$ orbits. We argue that to ready the GW community for the sensitivity of future detectors, numerical relativity groups must be aware of this caveat, and also run future simulations with at least three resolutions to properly assess waveform accuracy. 

Abstract We present a major update to the Simulating eXtreme Spacetimes (SXS) Collaboration’s catalog of binary black hole simulations. Using highly efficient spectral methods implemented in the Spectral Einstein Code (SpEC), we have nearly doubled the total number of binary configurations from 2,018 to 3,756. The catalog now more densely covers the parameter space with precessing simulations up to mass ratio q = 8 and dimensionless spins up to |χ⃗| ≤ 0.8 with near-zero eccentricity. The catalog also includes some simulations at higher mass ratios with moderate spin and more than 250 eccentric simulations. We have also deprecated and rerun some simulations from our previous catalog (e.g., simulations run with a much older version of SpEC or that had anomalously high errors in the waveform). The median waveform difference (which is similar to the mismatch) between resolutions over the simulations in the catalog is 4 × 10−4. The simulations have a median of 22 orbits, while the longest simulation has 148 orbits. We have corrected each waveform in the catalog to be in the binary’s center-of-mass frame and exhibit gravitational-wave memory. We estimate the total CPU cost of all simulations in the catalog to be 480,000,000 core-hours. We find that using spectral methods for binary black hole simulations is over 1,000 times more efficient than previously published finite-difference simulations. The full catalog is publicly available through the sxs Python package and at https://data.black-holes.org . 

Abstract When numerically solving Einstein’s equations for the evolution of binary black holes, physical imperfections in the initial data manifest as a transient, high-frequency pulse of ‘junk radiation.’ This unphysical signal must be removed before the waveform can be used. Improvements in the efficiency of numerical simulations now allow waveform catalogs containing thousands of waveforms to be produced. Thus, an automated procedure for identifying junk radiation is required. To this end, we present a new algorithm based on the empirical mode decomposition (EMD) from the Hilbert–Huang transform. This approach allows us to isolate and measure the high-frequency oscillations present in the measured irreducible masses of the black holes. The decay of these oscillations allows us to estimate the time from which the junk radiation can be ignored. To make this procedure more precise, we propose three distinct threshold criteria that specify how small the contribution of junk radiation has to be before it can be considered negligible. We apply this algorithm to 3403 BBH simulations from the Simulating eXtreme Spacetime catalog to find appropriate values for the thresholds in the three criteria. We find that this approach yields reliable decay time estimates, i.e. when to consider the simulation physical, for $>$98.5% of the simulations studied. This demonstrates the efficacy of the EMD as a suitable tool to automatically isolate and characterize junk radiation in the simulation of binary black hole systems. 

Abstract Cauchy-characteristic evolution (CCE) is a powerful method for accurately extracting gravitational waves at future null infinity. In this work, we extend the previously implemented CCE system within the numerical relativity code SpECTRE by incorporating a scalar field. This allows the system to capture features of beyond-general-relativity theories. We derive scalar contributions to the equations of motion, Weyl scalar computations, Bianchi identities, and balance laws at future null infinity. Our algorithm, tested across various scenarios, accurately reveals memory effects induced by both scalar and tensor fields and captures Price’s power-law tail ( $u^{-l-2}$) in scalar fields at future null infinity, in contrast to the $t^{-2l-3}$tail at future timelike infinity. 

Abstract Gravitational memory effects and the BMS freedoms exhibited at future null infinity have recently been resolved and utilized in numerical relativity simulations. With this, gravitational wave models and our understanding of the fundamental nature of general relativity have been vastly improved. In this paper, we review the history and intuition behind memory effects and BMS symmetries, how they manifest in gravitational waves, and how controlling the infinite number of BMS freedoms of numerical relativity simulations can crucially improve the waveform models that are used by gravitational wave detectors. We reiterate the fact that, with memory effects and BMS symmetries, not only can these next-generation numerical waveforms be used to observe never-before-seen physics, but they can also be used to test GR and learn new astrophysical information about our Universe. 

Abstract We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods. 

Abstract Binary black holes are the most abundant source of gravitational-wave observations. Gravitational-wave observatories in the next decade will require tremendous increases in the accuracy of numerical waveforms modeling binary black holes, compared to today’s state of the art. One approach to achieving the required accuracy is using spectral-type methods that scale to many processors. Using theSpECTREnumerical-relativity (NR) code, we present the first simulations of a binary black hole inspiral, merger, and ringdown using discontinuous Galerkin (DG) methods. The efficiency of DG methods allows us to evolve the binary through ∼ 18 orbits at reasonable computational cost. We then useSpECTRE’s Cauchy Characteristic Evolution (CCE) code to extract the gravitational waves at future null infinity. The open-source nature ofSpECTREmeans this is the first time a spectral-type method for simulating binary black hole evolutions is available to the entire NR community. 

One of the most promising avenues to perform numerical evolutions in theories beyond general relativity is the approach, a proposal in which new “driver” equations are added to the evolution equations in a way that allows for stable numerical evolutions. In this direction, we extend the numerical relativity code p to evolve a “fixed” version of scalar Gauss-Bonnet theory in the decoupling limit, a phenomenologically interesting theory that allows for hairy black hole solutions in vacuum. We focus on isolated black hole systems both with and without linear and angular momentum, and propose a new driver equation to improve the recovery of such stationary solutions. We demonstrate the effectiveness of the latter by numerically evolving black holes that undergo spontaneous scalarization using different driver equations. Finally, we evaluate the accuracy of the obtained solutions by comparing with the original unaltered theory. Published by the American Physical Society2024 

Abstract We analyze the directional dependence of the gravitational wave (GW) emission from 15 3D neutrino radiation hydrodynamic simulations of core-collapse supernovae (CCSNe). Using spin weighted spherical harmonics, we develop a new analytic technique to quantify the evolution of the distribution of GW emission over all angles. We construct a physics-informed toy model that can be used to approximate GW distributions for general ellipsoid-like systems, and use it to provide closed form expressions for the distribution of GWs for different CCSN phases. Using these toy models, we approximate the protoneutron star (PNS) dynamics during multiple CCSN stages and obtain similar GW distributions to simulation outputs. When considering all viewing angles, we apply this new technique to quantify the evolution of preferred directions of GW emission. For nonrotating cases, this dominant viewing angle drifts isotropically throughout the supernova, set by the dynamical timescale of the PNS. For rotating cases, during core bounce and the following tens of milliseconds, the strongest GW signal is observed along the equator. During the accretion phase, comparable—if not stronger—GW amplitudes are generated along the axis of rotation, which can be enhanced by the lowT/∣W∣ instability. We show two dominant factors influencing the directionality of GW emission are the degree of initial rotation and explosion morphology. Lastly, looking forward, we note the sensitive interplay between GW detector site and supernova orientation, along with its effect on detecting individual polarization modes.