Tarnished by Tools: Cost of Systematics in Golden Dark Siren Cosmology

Abstract

Golden dark sirens - exceptionally well-localized gravitational-wave (GW) sources without electromagnetic counterparts - offer a powerful route to precision measurements of the Hubble constant, $H_0$, with next-generation (XG) detectors. The statistical promise of this method, however, places stringent demands on waveform accuracy and detector calibration, as even small systematic errors can dominate over statistical uncertainties at high signal-to-noise ratios. We investigate the impact of waveform-modeling systematics on golden dark siren cosmology using a synthetic population of binary black holes consistent with current GW observations and analyzed in the XG-detector era. By comparing state-of-the-art waveform models against numerical-relativity-based reference signals, we quantify modeling inaccuracies from both modeling and data-analysis perspectives and assess how they propagate into biases in luminosity distance, host-galaxy association, and single-event $H_0$ inference. We find that while current waveform models often allow recovery of statistically consistent $H_0$ posteriors, small waveform-induced biases can significantly affect three-dimensional localization and host galaxy ranking, occasionally leading to incorrect redshift assignments. We further derive order-of-magnitude requirements on detector calibration accuracy needed to ensure that calibration systematics remain subdominant for golden dark sirens observed with XG networks. To realize sub-percent $H_0$ measurements with golden dark sirens will require waveform and calibration accuracies that scale as $\mathcal{O}(ρ^{-2})$ with signal-to-noise ratio, motivating sustained advances in waveform modeling, numerical relativity, and detector calibration for the XG era.

Figures (8)

• Figure 1: Waveform unfaithfulness for a simulated population of golden dark sirens, evaluated from a modeller's perspective. Top panel: Distribution of extrinsic-parameter–maximized unfaithfulness, $\bar{\mathcal{F}}_{\boldsymbol{\theta}_{\rm ext}}$ for three different waveform models SEOBNRv5PHM (blue), TEOBResumS-GIOTTO (red), and IMRPhenomXPNR (green)—computed against the reference signal population simulated using NRHybSur3dq8. Bottom panel: Event-by-event unfaithfulness projected across the intrinsic parameter space, shown as functions of detector-frame total mass $M_T^{\rm det}$, mass ratio $q = m_1/m_2 \geq 1$ and effective inspiral spin parameter $\chi_{\rm eff}$. Each column represents a different waveform family. Colors indicate the value of $\bar{\mathcal{F}}_{\boldsymbol{\theta}_{\rm ext}}$, highlighting regions of parameter space where modelling systematics are most pronounced. The black-dashed lines encompass $68\%$ of the simulated population.
• Figure 2: Waveform unfaithfulness for a simulated population of golden dark sirens, evaluated from a data‑analysis perspective. The solid curve shows the distribution of $\bar{\mathcal{F}}$ for SEOBNRv5PHM when compared against NRHybSur3dq8, while the curve with overlaid black dashed lines on top shows the corresponding distribution for IMRPhenomXPNR. The color scale indicates the snr at which waveform systematics would fail to recover the true binary parameters within their 90% credible level.
• Figure 3: Representative whitened sky localizations for IMRPhenomXPNR recoveries at comparable luminosity distance $D_L$. The true host galaxy is marked by intersecting black lines, while other candidate host galaxies are color-coded by their luminosity-distance offset relative to the inferred $D_L$, in units of the posterior standard deviation $\sigma_{d_L}$. Grey contours indicate the $|\boldsymbol{\Theta}|=1\sigma,\,2\sigma,$ and $3\sigma$ regions, and the red circle encloses the 90% credible sky area $\Sigma_{90}$. From left to right, the panels illustrate a golden siren with a unique host, two copper sirens with $<10$ plausible hosts at similar distances, and a classical dark siren with several viable counterparts.
• Figure 4: $H_0$ posterior distribution for recovery with IMRPhenomXPNR. Association probability shown with colorscale and opacity. True (simulated) counterpart hatched. Injected $H_0=67.7 ~\text{km}/\text{s}/\text{Mpc}$ marked with the vertical line.
• Figure 5: Characteristic frequency-dependent calibration tolerance $Y(f_k)$ for representative golden dark siren binary population observed with ce40, ce20 and et (harmonic-mean). The solid red curve shows the median behavior while the shaded region indicates the 90% spread across the signal population. For comparison, the current Advanced LIGO detectors typically have both amplitude and phase calibration uncertainty at $\sim 10^{-2}$ level Capote:2024rmo.