Session L16: Gravitational Waveform Modeling of Compact Binaries I

Live

Gravitational waves emitted by inner binaries in hierarchical triples are interesting astrophysical candidates for space-based detectors like LISA. In the presence of a third body, the inner binary undergoes oscillations in eccentricity and inclination angle due to the Kozai-Lidov (KL) mechanism. In this talk, I will discuss how to construct analytic gravitational waveforms in the Fourier domain, with this effect included. Using multiple-scale analysis, we make use of the separability of timescales in the system to combine the effects of KL oscillations and radiation reaction. The imprint on the waveform, due to this combined evolution, can then be analytically computed in the stationary phase approximation. I will also discuss our analysis of the parameters of the hierarchical triple which can produce a detectable (by LISA) imprint of KL oscillations on the waveform and outline potential implications for gravitational wave data analysis and tests of GR.   

Live

To date, gravitational wave detections have been limited to those from quasi-circular binary mergers. However, a significant percentage of mergers could have measurable residual eccentricities, resulting from either external perturbations of the system or short timescales between formation and merger of the binary. Understanding how the orbits of such binaries evolve could aid in creating useful eccentric gravitational waveform templates as well as provide astrophysical information about the environment and formation channels of these systems. We have analyzed the long-term evolution of non-spinning, highly eccentric binaries of general mass ratios, incorporating gravitational radiation reaction at 4.5 post-Newtonian order, including leading tail effects. We have developed accurate analytic expressions for the binary’s eccentricity and total inspiral time as a function of its late-time gravitational wave frequency, and of its initial energy and angular momentum. We will discuss our results and their implications for eccentric binary gravitational wave detection.   

Live

Close white dwarf binaries are promising sources of gravitational-wave signals for Laser Interferometer Space Antenna (LISA). The eccentricity of such a system decays over time due to gravitational-wave emission and tidal friction. In some scenarios, however, the orbits can have a high eccentricity even at the late stage of inspiral. Examples are hierarchical triple systems involving gravitational interactions between the binary and a distant third body. Analyzing the gravitational-wave signals from these systems requires accurate waveform templates. In this talk, I will describe a new waveform model for eccentric binary white dwarf systems taking tides into account. We propose a semi-analytical ``kludge model'' which gives the quadrupole radiation from a post-Keplerian orbit (obtained numerically) including the post-1-Newtonian effect on point masses as well as the quadrupolar tidal force. We also separately compare the effects on orbital evolution due to various factors including gravitational-wave emission, the additional force on the orbit due to tidally-induced quadrupoles, and the effect of tidal friction. The model aims to provide accurate and efficient templates to study eccentric binary white dwarf systems with LISA.   

Live

We develop new strategies to build numerical relativity surrogate models for eccentric binary black hole systems, which are expected to play an increasingly important role in current and future gravitational-wave detectors. We introduce a new surrogate waveform model, \texttt{NRSur2dq1Ecc}, using 47 nonspinning, equal-mass waveforms with eccentricities up to $0.2$ when measured at a reference time of $5500M$ before merger. This is the first waveform model that is directly trained on eccentric numerical relativity simulations and does not require that the binary circularizes before merger. The model includes the $(2,2)$, $(3,2)$, and $(4,4)$ spin-weighted spherical harmonic modes. We show that our waveform model can accurately predict numerical relativity waveforms with mismatches $\approx10^{-3}$. We demonstrate that the waveform model can also recover subtle effects like mode-mixing in the ringdown signal without any special ad-hoc modeling steps. Finally, we show that despite being trained only on equal-mass binaries, \texttt{NRSur2dq1Ecc} can be reasonably extended up to mass ratio $q\approx3$ with mismatches $\simeq 10^{-2}$ for eccentricities smaller than $\sim 0.05$ as measured at a reference time of $2000M$ before merger.   

Live

Gravitational wave data analysis relies on accurate and efficient waveform models which incorporate physical phenomena such as precession and higher-order modes. Current semi-analytical models for precessing binary black holes are not calibrated to numerical relativity in the precessing sector, in part due to the high-dimensionality of the parameter space. One possibility lies in dimensional reduction of the precessing spin-space, previously done with $\chi_p$, but it has been shown that $\chi_p$ does not accurately represent precessing higher-order modes, which are crucial for modelling a complete precessing waveform. In this talk, I will present an alternative 2D effective precession spin $\vec{\chi}_{\perp}$. I will show that it reproduces the precession dynamics and higher-order modes of strong-field precessing waveforms much more accurately than $\chi_p$, as well as the remnant spin. This could be a promising avenue towards meaningful calibration of semi-analytic precessing, higher-order mode waveforms to numerical relativity.   

Live

Accurate modelling of gravitational waves from compact binaries is essential for their detection and parameter estimation. The accuracy is generally measured by comparison to Numerical Relativity (NR). We present supplementary methods to test for consistency with exact General Relativity using balance laws: an infinite tower of supermomentum balance laws and the angular momentum balance law. These methods do not rely on NR and can thus be used all across parameter space. The supermomentum balance law cannot be applied directly, however, since currently the memory effect is not modeled. Instead we use it indirectly to first \emph{infer} the memory and then compare the systematic differences of the inferred memory to their statistical uncertainties. We apply these methods to some recent models and binary black hole events.   

Live

While most binary mergers are expected to circularize when they enter the LIGO/Virgo frequency band, a small fraction of those binaries could have non-negligible orbital eccentricity depending on their formation channel. Hence, it is important to accurately model eccentricity effects in waveform models to detect those binaries, infer their properties and shed light on their astrophysical environment. In this talk, I will present a multipolar effective-one-body (EOB) eccentric waveform model for spin-aligned black holes. In the quasi-circular orbit limit, it reproduces the state-of-the-art EOB model currently used in LIGO/Virgo analyses (SEOBNRv4HM). The waveform model contains eccentricity effects in the radiation-reaction force and gravitational modes through second post-Newtonian order, including tail effects, spin-orbit, and spin-spin couplings. I will also present results that validate such an eccentric waveform model against numerical-relativity simulations.   

Live

In the era of high-precision gravitational wave (GW) astronomy, modeling error may routinely dominate over statistical error as GW detectors approach design sensitivity. Due to the expected increase in the signal-to-noise ratio of future detections, models that provide uncertainty estimates across the parameter space should play an increasingly important role in the analysis effort. For example, the inclusion of these uncertainties into the analysis will improve confidence in parameter estimates of future GW events. In this talk, I will discuss current efforts in the development of an error estimation methodology for surrogate waveform models. We apply this methodology to a set of benchmark test cases to verify the theoretical framework and implement the framework to non-spinning surrogate models.   

Live

The recent detection of GW190814 highlights the need for reliable, high-accuracy gravitational waveform templates for binary black holes of high mass ratios. We describe NRHybSur2dq15, a surrogate model for hybridized, non-precessing numerical relativity (NR) waveforms, extending the previously explored mass ratio ranges. In this model, we train the surrogate over two parameters: the mass ratio, $q\in[1,15]$, and the spin of the higher-mass black hole, $\left|\chi^1_z\right|\leq 0.8$. For the training, we use hybrid waveforms generated from the NR simulations. The new surrogate model reproduces the hybrid waveforms with reasonable mismatches over the entire LIGO band for stellar-mass binaries. The surrogate model also is quite robust to extrapolations of the parameters. Finally, we use templates generated from the surrogate model for parameter estimation of GW190814.