Surrogate model of hybridized numerical relativity binary black hole waveforms

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Abstract

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 Hz) for stellar mass binaries with total masses as low as $2.25\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. We include the $\ensuremath{\ell}\ensuremath{\le}4$ 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 $q\ensuremath{\le}8$, and $|{\ensuremath{\chi}}_{1z}|,|{\ensuremath{\chi}}_{2z}|\ensuremath{\le}0.8$, where ${\ensuremath{\chi}}_{1z}$ (${\ensuremath{\chi}}_{2z}$) is the spin of the heavier (lighter) black hole in the direction of orbital angular momentum. The surrogate reproduces the hybrid waveforms accurately, with mismatches $\ensuremath{\lesssim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ over the mass range $2.25\text{ }\text{ }{M}_{\ensuremath{\bigodot}}\ensuremath{\le}M\ensuremath{\le}300\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. At high masses ($M\ensuremath{\gtrsim}40\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$), where the merger and ringdown are more prominent, we show roughly 2 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.

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