Computing fast and reliable gravitational waveforms of binary neutron star merger remnants

Gravitational waves have been detected from the inspiral of a binary neutron-star, GW170817, which allowed constraints to be placed on the neutron star equation of state. The equation of state can be further constrained if gravitational waves from a postmerger remnant are detected. Postmerger waveforms are currently generated by numerical-relativity simulations, which are computationally expensive. Here we introduce a hierarchical model trained on numerical-relativity simulations, which can generate reliable postmerger spectra in a fraction of a second. Our spectra have mean fitting factors of 0.95, which compares to a fitting factor of 0.93 between different numerical-relativity codes that simulate the same physical system. This method is the first step towards generating large template banks of spectra for use in postmerger detection and parameter estimation.

Figure 1

Reconstructed gravitational-wave spectra generated with leave-one-out cross-validation (solid red curve) and original numerical-relativity spectra [17] (dashed black curve), scaled to a distance of 50 Mpc. Each column represents a different equation of state and each row represents a different neutron star mass, increasing towards the bottom. The one-sigma uncertainty in the spectra is shaded in light red for each prediction. The Advanced LIGO noise amplitude spectral density (dotted black curve) [34] is shown on all subplots. A numerical-relativity spectrum generated from [22] is shown (dashed dot blue curve) in the last row (equal mass $1.35{\mathrm{M}}_{\odot }$) for SLy [37] (fourth column) equation of state.

Figure 2

Histogram of fitting factors determined by comparing numerical-relativity spectra with spectra generated by our model using leave-one-out cross-validation.

Figure 3

Spectra generated by the model when trained on all the numerical-relativity spectra (red curve). The uncertainties in the spectra are shown in light red. The Advanced LIGO noise amplitude spectral density (dotted black line) is shown on all subplots.

Figure 4

Fitting factor between spectra generated using our hierarchical model with $1.30{\mathrm{M}}_{\odot }$ and ${\kappa }_2^{\tau }=100$ (black cross), against a grid of mass and quadrupolar tidal coupling constant values.