The High-Mass-Ratio Challenge in Gravitational Waveform Modelling

Abstract

Binary black hole (BBH) mergers detected via gravitational waves are addressing key open questions in astrophysics, cosmology, and fundamental physics. Our scientific conclusions rely on extracting accurate source parameters, for which we require accurate signal modelling. It is well known that current BBH waveform models need to be improved for high-mass-ratio, strongly precessing systems, and in this paper we provide a concrete illustration of this issue, showing that the degradation in model performance is substantially more severe than might have been anticipated. We present numerical relativity (NR) simulations of precessing BBH systems with a mass ratio of 18 and a dimensionless spin of 0.8 on the larger black hole (with the smaller black hole non-spinning), covering five values of spin misalignment. We assess the accuracy of state-of-the-art waveform models in this region of parameter space by computing the standard mismatch between the models and the NR waveforms. We find that all current waveform models often exhibit significant mismatches ($\gtrsim$0.1), indicating poor performance in this regime. We also perform limited parameter estimation using a subset of state-of-the-art waveform models, injecting these NR simulations as signals into the three-detector LIGO-Virgo network. In some cases we find errors in mass measurements of over 100%, dramatically illustrating that substantial improvements are required in existing waveform models. The numerical simulations presented here will be valuable for calibrating future BBH waveform models in this region of parameter space.

Figures (11)

• Figure 1: The plus GW polarization of each of our NR simulations, with redshifted total mass $150 M_{\odot}$, $\theta_{\mathrm{LN}}=30^\circ$, and $D_L=300$ Mpc. The five panels show each choice of spin misalignment: $\theta_{\rm LS_1}=30^\circ, 60^\circ,\, 90^\circ,\, 120^\circ,\, 150^\circ$. The waveforms have been tapered to remove junk radiation.
• Figure 2: Mismatch between NR waveforms for CF_81 configuration ($\{q,\, \chi_1,\, \theta_{\mathrm{LS}_{1}} \}=\{18, 0.8, 30^\circ \}$) at different numerical resolutions as a function of the binary inclination angle $\theta_{\rm LN}$ (angle between the line of sight and the initial orbital angular momentum) at redshifted total mass $150 M_{\odot}$. The mismatch is optimized over luminosity distance, coalescence time and phase, sky location, and polarization. Each solid marker denotes the SNR-weighted mismatch, while the vertical lines show the range between the minimum and maximum mismatch obtained across the sampled signal polarizations and phases (see text for details).
• Figure 3: Mismatch between NR waveforms for ${\tt CF\_{81}}$ configuration in Table \ref{['table:metadata']} at different extraction radii (as indicated in the legend) as a function of the binary inclination angle $\theta_{\rm LN}$ at redshifted total masses of $150 M_{\odot}$. The parameters over which the mismatch is optimized, as well as the plotting style and interpretation, are the same as in Fig. \ref{['fig:NRNR_Mismatch_Theta_LS_30_Mtot_150']}.
• Figure 4: Plus polarization of NR simulations and three contemporary waveform models, XPNR, TPHM, and v5PHM. Redshifted total mass is $150 M_{\odot}$, $\theta_{\mathrm{LN}}=30^\circ$, and $D_L=300$ Mpc (with the polarization angle chosen to be zero). Top: NR simulation ${\tt CF\_{81}}$ ($\theta_{\rm LS_1} = 30^\circ$). Bottom: ${\tt CF\_{85}}$ ($\theta_{\rm LS_1} = 150^\circ$). The XPNR (blue dashed), TPHM (green dash-dotted), and v5PHM (orange dotted ) models show significant disagreement with the underlying NR data (solid black).
• Figure 5: Mismatches against three current models. The spin misalignment angle $\theta_{\rm LS_{1}}$ of each simulation is indicated on the $x$-axis. The range of values corresponds to variations in inclination, polarisation and reference phase. Top: mismatches restricted to $\ell =2$ modes of both the NR waveforms and the waveform models. Bottom: all available modes in both NR and model.