# Surrogate model of hybridized numerical relativity binary black hole waveforms

## TL;DR

This paper introduces NRHybSur3dq8, a fast and accurate surrogate model for hybridized binary black hole waveforms that covers the entire LIGO frequency band, enabling improved gravitational wave data analysis.

## Contribution

The paper presents a novel surrogate model trained on hybridized waveforms, extending the validity to the full LIGO band and including higher modes, with high accuracy and applicability to a wide parameter space.

## Key findings

- Surrogate model achieves mismatches less than 3e-4 across the mass range.
- Significant improvement over existing models at high masses.
- Model accurately reproduces mode mixing in the ringdown phase.

## 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 $20~\text{Hz}$) 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 $q\leq8$, 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 $\lesssim 3\times10^{-4}$ over the mass range $2.25M_{\odot} \leq M \leq 300 M_{\odot}$. At high masses ($M\gtrsim40M_{\odot}$), 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.