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Register a new userA Precessing Numerical Relativity Waveform Surrogate Model for Binary Black Holes: A Gaussian Process Regression Approach
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Gravitational wave astrophysics relies heavily on the use of matched filtering both to detect signals in noisy data from detectors, and to perform parameter estimation on those signals. Matched filtering relies upon prior knowledge of the signals expected to be produced by a range of astrophysical systems, such as binary black holes. These waveform signals can be computed using numerical relativity techniques, where the Einstein field equations are solved numerically, and the signal is extracted from the simulation. Numerical relativity simulations are, however, computationally expensive, leading to the need for a surrogate model which can predict waveform signals in regions of the physical parameter space which have not been probed directly by simulation. We present a method for producing such a surrogate using Gaussian process regression which is trained directly on waveforms generated by numerical relativity. This model returns not just a single interpolated value for the waveform at a new point, but a full posterior probability distribution on the predicted value. This model is therefore an ideal component in a Bayesian analysis framework, through which the uncertainty in the interpolation can be taken into account when performing parameter estimation of signals.
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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.
The recent observation of GW190412, the first high-mass ratio binary black-hole (BBH) merger, by the LIGO-Virgo Collaboration (LVC) provides a unique opportunity to probe the impact of subdominant harmonics and precession effects encoded in a gravitational wave signal. We present refined estimates of source parameters for GW190412 using texttt{NRSur7dq4}, a recently developed numerical relativity waveform surrogate model that includes all $ell leq 4$ spin-weighted spherical harmonic modes as well as the full physical effects of precession. We compare our results with two different variants of phenomenological precessing BBH waveform models, texttt{IMRPhenomPv3HM} and texttt{IMRPhenomXPHM}, as well as to the LVC results. Our results are broadly in agreement with texttt{IMRPhenomXPHM} results and the reported LVC analysis compiled with the texttt{SEOBNRv4PHM} waveform model, but in tension with texttt{IMRPhenomPv3HM}. Using the texttt{NRSur7dq4} model, we provide a tighter constraint on the mass-ratio ($0.26^{+0.08}_{-0.06}$) as compared to the LVC estimate of $0.28^{+0.13}_{-0.07}$ (both reported as median values withs 90% credible intervals). We also constrain the binary to be more face-on, and find a broader posterior for the spin precession parameter. We further find that even though $ell=4$ harmonic modes have negligible signal-to-noise ratio, omission of these modes will influence the estimated posterior distribution of several source parameters including chirp mass, effective inspiral spin, luminosity distance, and inclination. We also find that commonly used model approximations, such as neglecting the asymmetric modes (which are generically excited during precession), have negligible impact on parameter recovery for moderate SNR-events similar to GW190412.
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.
We construct a new factorized waveform including $(l,|m|)=(2,2),(2,1),(3,3),(4,4)$ modes based on effective-one-body (EOB) formalism, which is valid for spinning binary black holes (BBH) in general equatorial orbit. When combined with the dynamics of $texttt{SEOBNRv4}$, the $(l,|m|)=(2,2)$ mode waveform generated by this new waveform can fit the original $texttt{SEOBNRv4}$ waveform very well in the case of a quasi-circular orbit. We have calibrated our new waveform model to the Simulating eXtreme Spacetimes (SXS) catalog. The comparison is done for BBH with total mass in $(20,200)M_odot$ using Advanced LIGO designed sensitivity. For the quasi-circular cases we have compared our $(2,2)$ mode waveforms to the 281 numerical relativity (NR) simulations of BBH along quasi-circular orbits. All of the matching factors are bigger than 98%. For the elliptical cases, 24 numerical relativity simulations of BBH along an elliptic orbit are used. For each elliptical BBH system, we compare our modeled gravitational polarizations against the NR results for different combinations of the inclination angle, the initial orbit phase and the source localization in the sky. We use the the minimal matching factor respect to the inclination angle, the initial orbit phase and the source localization to quantify the performance of the higher modes waveform. We found that after introducing the high modes, the minimum of the minimal matching factor among the 24 tested elliptical BBHs increases from 90% to 98%. Following our previous $texttt{SEOBNRE}$ waveform model, we call our new waveform model $texttt{SEOBNREHM}$. Our $texttt{SEOBNREHM}$ waveform model can match all tested 305 SXS waveforms better than 98% including highly spinning ($chi=0.99$) BBH, highly eccentric ($eapprox0.15$) BBH and large mass ratio ($q=10$) BBH.
When two black holes merge, a tremendous amount of energy is released in the form of gravitational radiation in a short span of time, making such events among the most luminous phenomenon in the universe. Models that predict the peak luminosity of black hole mergers are of interest to the gravitational wave community, with potential applications in tests of general relativity. We present a surrogate model for the peak luminosity that is directly trained on numerical relativity simulations of precessing binary black holes. Using Gaussian process regression, we interpolate the peak luminosity in the 7-dimensional parameter space of precessing binaries with mass ratios $qleq4$, and spin magnitudes $chi_1,chi_2leq0.8$. We demonstrate that our errors in estimating the peak luminosity are lower than those of existing fitting formulae by about an order of magnitude. In addition, we construct a model for the peak luminosity of aligned-spin binaries with mass ratios $qleq8$, and spin magnitudes $|chi_{1z}|,|chi_{2z}|leq0.8$. We apply our precessing model to infer the peak luminosity of the GW event GW190521, and find the results to be consistent with previous predictions.
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