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Register a new userMatching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries
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We present a new phenomenological gravitational waveform model for the inspiral and coalescence of non-precessing spinning black hole binaries. Our approach is based on a frequency domain matching of post-Newtonian inspiral waveforms with numerical relativity based binary black hole coalescence waveforms. We quantify the various possible sources of systematic errors that arise in matching post-Newtonian and numerical relativity waveforms, and we use a matching criteria based on minimizing these errors; we find that the dominant source of errors are those in the post-Newtonian waveforms near the merger. An analytical formula for the dominant mode of the gravitational radiation of non-precessing black hole binaries is presented that captures the phenomenology of the hybrid waveforms. Its implementation in the current searches for gravitational waves should allow cross-checks of other inspiral-merger-ringdown waveform families and improve the reach of gravitational wave searches.
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We present the first analytical inspiral-merger-ringdown gravitational waveforms from binary black holes (BBHs) with non-precessing spins, that is based on a description of the late-inspiral, merger and ringdown in full general relativity. By matching a post-Newtonian description of the inspiral to a set of numerical-relativity simulations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BBH coalescence, including a considerable fraction of precessing binaries in the comparable-mass regime, thus significantly improving the expected detection rates.
Numerical relativity (NR) simulations provide the most accurate binary black hole gravitational 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. However, NR-based surrogate models are limited by the training waveforms length, which is typically about 20 orbits before merger. We remedy this by hybridizing the NR waveforms using both post-Newtonian and effective one body waveforms for the early inspiral. We present NRHybSur3dq8, a surrogate model for hybridized nonprecessing numerical relativity waveforms, that is valid for the entire LIGO band (starting at $20~text{Hz}$) for stellar mass binaries with total masses as low as $2.25,M_{odot}$. We include the $ell leq 4$ and $(5,5)$ spin-weighted spherical harmonic modes but not the $(4,1)$ or $(4,0)$ modes. This model has been trained against hybridized waveforms based on 104 NR waveforms with mass ratios $qleq8$, and $|chi_{1z}|,|chi_{2z}| leq 0.8$, where $chi_{1z}$ ($chi_{2z}$) is the spin of the heavier (lighter) BH in the direction of orbital angular momentum. The surrogate reproduces the hybrid waveforms accurately, with mismatches $lesssim 3times10^{-4}$ over the mass range $2.25M_{odot} leq M leq 300 M_{odot}$. At high masses ($Mgtrsim40M_{odot}$), where the merger and ringdown are more prominent, we show roughly two orders of magnitude improvement over existing waveform models. We also show that the surrogate works well even when extrapolated outside its training parameter space range, including at spins as large as 0.998. Finally, we show that this model accurately reproduces the spheroidal-spherical mode mixing present in the NR ringdown signal.
A generic, non-eccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by 7 intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einsteins equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BBHs including all $7$ dimensions of the intrinsic non-eccentric parameter space. The surrogate model, which we call NRSur7dq2, is built from the results of $744$ numerical relativity simulations. NRSur7dq2 covers spin magnitudes up to $0.8$ and mass ratios up to $2$, includes all $ell leq 4$ modes, begins about $20$ orbits before merger, and can be evaluated in $sim~50,mathrm{ms}$. We find the largest NRSur7dq2 errors to be comparable to the largest errors in the numerical relativity simulations, and more than an order of magnitude smaller than the errors of other waveform models. Our model, and more broadly the methods developed here, will enable studies that would otherwise require millions of numerical relativity waveforms, such as parameter inference and tests of general relativity with GW observations.
We study the effectiveness of stationary-phase approximated post-Newtonian waveforms currently used by ground-based gravitational-wave detectors to search for the coalescence of binary black holes by comparing them to an accurate waveform obtained from numerical simulation of an equal-mass non-spinning binary black hole inspiral, merger and ringdown. We perform this study for the Initial- and Advanced-LIGO detectors. We find that overlaps between the templates and signal can be improved by integrating the match filter to higher frequencies than used currently. We propose simple analytic frequency cutoffs for both Initial and Advanced LIGO, which achieve nearly optimal matches, and can easily be extended to unequal-mass, spinning systems. We also find that templates that include terms in the phase evolution up to 3.5 pN order are nearly always better, and rarely significantly worse, than 2.0 pN templates currently in use. For Initial LIGO we recommend a strategy using templates that include a recently introduced pseudo-4.0 pN term in the low-mass ($M leq 35 MSun$) region, and 3.5 pN templates allowing unphysical values of the symmetric reduced mass $eta$ above this. This strategy always achieves overlaps within 0.3% of the optimum, for the data used here. For Advanced LIGO we recommend a strategy using 3.5 pN templates up to $M=12 MSun$, 2.0 pN templates up to $M=21 MSun$, pseudo-4.0 pN templates up to $65 MSun$, and 3.5 pN templates with unphysical $eta$ for higher masses. This strategy always achieves overlaps within 0.7% of the optimum for Advanced LIGO.
The production of numerical relativity waveforms that describe quasicircular binary black hole mergers requires high-quality initial data, and an algorithm to iteratively reduce residual eccentricity. To date, these tools remain closed source, or in commercial software that prevents their use in high performance computing platforms. To address these limitations, and to ensure that the broader numerical relativity community has access to these tools, herein we provide all the required elements to produce high-quality numerical relativity simulations in supercomputer platforms, namely: open source parameter files to numerical simulate spinning black hole binaries with asymmetric mass-ratios; open source $texttt{Python}$ tools to produce high-quality initial data for numerical relativity simulations of spinning black hole binaries on quasi-circular orbits; open source $texttt{Python}$ tools for eccentricity reduction, both as stand-alone software and deployed in the $texttt{Einstein Toolkit}$s software infrastructure. This open source toolkit fills in a critical void in the literature at a time when numerical relativity has an ever increasing role in the study and interpretation of gravitational wave sources. As part of our community building efforts, and to streamline and accelerate the use of these resources, we provide tutorials that describe, step by step, how to obtain and use these open source numerical relativity tools.
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