Systematic Biases in Estimating the Properties of Black Holes Due to Inaccurate Gravitational-Wave Models

TL;DR

The paper evaluates systematic biases in BBH parameter estimation arising from inaccuracies in state-of-the-art GW waveform models by injecting SEOBNRv5PHM signals and recovering them with IMRPhenomXPHM across LVK-like and XG detector networks. It combines Bayesian parameter estimation with linear-signal approximation (LSA) to quantify measurement errors and model-induced biases, and uses hierarchical Bayesian methods to assess population-level impacts. The main findings show robust recovery of the mass distribution but significant biases in spins, with biases increasing with detector-frame mass, mass ratio asymmetry, and precession, potentially affecting Hubble constant inferences, the edges of mass gaps, and spin-formation diagnostics, especially for next-generation detectors. The work highlights the critical need for continued NR calibration and waveform-model marginalization to realize precision GW astronomy, and documents bias-horizon concepts and the differential impact across detector networks.

Abstract

Gravitational-wave (GW) observations of binary black-hole (BBH) coalescences are expected to address outstanding questions in astrophysics, cosmology, and fundamental physics. Realizing the full discovery potential of upcoming LIGO-Virgo-KAGRA (LVK) observing runs and new ground-based facilities hinges on accurate waveform models. Using linear-signal approximation methods and Bayesian analysis, we start to assess our readiness for what lies ahead using two state-of-the-art quasi-circular, spin-precessing models: \texttt{SEOBNRv5PHM} and \texttt{IMRPhenomXPHM}. We ascertain that current waveforms can accurately recover the distribution of masses in the LVK astrophysical population, but not spins. We find that systematic biases increase with detector-frame total mass, binary asymmetry, and spin-precession, with most such binaries incurring parameter biases, extending up to redshifts $\sim3$ in future detectors. Furthermore, we examine three ``golden'' events characterized by large mass ratios, significant spin magnitudes, and high precession, evaluating how systematic biases may affect their scientific outcomes. Our findings reveal that current waveforms fail to enable the unbiased measurement of the Hubble-Lemaître parameter from loud signals, even for current detectors. Moreover, highly asymmetric systems within the lower BH mass-gap exhibit biased measurements of the secondary-companion mass, which impacts the physics of both neutron stars and formation channels. Similarly, we deduce that the primary mass of massive binaries ($ > 60 M_\odot$) will also be biased, affecting supernova physics. Future progress in analytical calculations and numerical-relativity simulations, crucial for calibrating the models, must target regions of the parameter space with significant biases to develop more accurate models. Only then can precision GW astronomy fulfill the promise it holds.

Figures (27)

• Figure 1: GW strains for a BBH system with parameters given in Table \ref{['tab:params']} (Binary 1) at the LIGO-Livingston detector of the O5 network. The black curve is the injected signal SEOBNRv5PHM, the green curve is the template IMRPhenomXPHM, evaluated for the injection parameters, and time shifted and global-phase rotated to maximize their overlap with the signal; the brown curve is the template IMRPhenomXPHM evaluated at the maximum likelihood values obtained using a Bayesian analysis. The reference for the time axis, $t=0$, is taken to be the peak of the GW multipole $h_{22}$ of the signal.
• Figure 2: Amplitude--spectral-density curves of the various detectors used in this paper (see footnote \ref{['curves']}). The curves labeled by A+ and V+ denote the design sensitivity of the LIGO and Virgo detectors, respectively, which form part of the network of the fifth observing run (O5), while A# refers to the LIGO detectors at upgraded sensitivity. The next-generation observatories are the ET and CE with the baseline network for the latter consisting of a 20-km and a 40-km detector.
• Figure 3: Comparison of the posterior distributions for the chirp mass, symmetric mass ratio, luminosity distance, and primary spin magnitude for Binary 1 with parameters given in Table \ref{['tab:params']} and in the O5 detector network. The distributions obtained from a Bayesian parameter estimation using Bilby are shown in green. The estimates from the LSA with and without the minimization procedure (\ref{['eq:mm']}) (alignment) are shown in orange and brown, respectively. The black cross-hairs show the true injected value. The parameter estimation is performed by injecting a SEOBNRv5PHM signal and recovering it with the IMRPhenomXPHM waveforms. The Bayesian posteriors are accurately represented by the LSA when the alignment is enforced.
• Figure 4: Distribution of component masses for a population of $10^5$BBH following the astrophysical distribution as determined by the LVK Collaboration.
• Figure 5: Distribution of the SNR of the $10^5$ BBHs simulated in the three detector networks computed using the IMRPhenomXPHM model. The SNR distribution is similar when using the SEOBNRv5PHM model. In shaded gray, we indicate the region with network-SNR threshold below 12.