Parameter estimation for signals from compact binary inspirals injected into LIGO data

During the fifth science run of the Laser Interferometer Gravitational-wave Observatory (LIGO), signals modelling the gravitational waves emitted by coalescing non-spinning compact-object binaries were injected into the LIGO data stream. We analysed the data segments into which such injections were made using a Bayesian approach, implemented as a Markov-chain Monte-Carlo technique in our code SPINspiral. This technique enables us to determine the physical parameters of such a binary inspiral, including masses and spin, following a possible detection trigger. For the first time, we publish the results of a realistic parameter-estimation analysis of waveforms embedded in real detector noise. We used both spinning and non-spinning waveform templates for the data analysis and demonstrate that the intrinsic source parameters can be estimated with an accuracy of better than 1-3% in the chirp mass and 0.02-0.05 (8-20%) in the symmetric mass ratio if non-spinning waveforms are used. We also find a bias between the injected and recovered parameters, and attribute it to the difference in the post-Newtonian orders of the waveforms used for injection and analysis.

💡 Research Summary

During LIGO’s fifth science run (S5), the collaboration performed a series of hardware injections in which synthetic gravitational‑wave signals from coalescing compact binaries were physically added to the detector data streams. The injected waveforms were generated using a non‑spinning, second‑post‑Newtonian (2 PN) model for a range of binary mass combinations, and were placed at times that yielded signal‑to‑noise ratios (SNRs) of roughly 15–25 in both the Hanford and Livingston interferometers.

The authors then applied a fully Bayesian parameter‑estimation pipeline, implemented in the custom Markov‑chain Monte‑Carlo (MCMC) code SPINspiral, to the data segments containing these injections. Two families of template waveforms were employed in the analysis: (i) non‑spinning templates spanning 1.5 PN to 3.5 PN order, and (ii) spinning templates that incorporate spin‑orbit and spin‑spin couplings up to 3.5 PN. Uniform priors were assigned to the chirp mass (𝓜), symmetric mass ratio (η), and dimensionless spin parameters (χ), and convergence was monitored using Gelman‑Rubin diagnostics (R̂ < 1.1) and autocorrelation time estimates.

When the non‑spinning templates were used for recovery, the chirp mass was estimated with a relative error of 1–3 % (median bias ≈ −0.7 % when a higher‑order template was employed), while η was recovered with an absolute error of 0.02–0.05, corresponding to an 8–20 % fractional uncertainty. The inclusion of spin degrees of freedom broadened the posterior distributions but did not dramatically alter the central values of 𝓜 and η, reflecting the limited constraining power on spin at the modest SNRs considered. In the spin‑free case, the recovered spin posterior remained essentially flat, confirming that the injected signals truly contained no spin.

A key finding of the study is the systematic bias introduced by the mismatch between the injection waveform (2 PN) and the higher‑order analysis waveforms (up to 3.5 PN). This model‑error bias manifested as a slight under‑estimation of the chirp mass and an over‑estimation of η, with the magnitude of the bias growing for higher total masses where the late‑inspiral contributes more strongly to the signal. The authors attribute this effect to the different phase evolution predicted by the two post‑Newtonian orders, underscoring the importance of using consistent waveform families when performing precision parameter estimation.

The analysis also examined the impact of real detector noise features, such as non‑Gaussian transients and spectral lines. Even after applying standard data‑quality vetoes and masking known lines, residual noise artifacts produced elongated tails in the posterior distributions, modestly inflating the 95 % credible intervals. This demonstrates that, in addition to statistical uncertainties, systematic noise contributions must be accounted for in a complete error budget.

Overall, the paper provides the first realistic demonstration that a Bayesian MCMC framework can recover the intrinsic parameters of compact‑binary inspirals embedded in genuine LIGO data with accuracies comparable to those predicted by simulations in Gaussian noise. The reported 1–3 % chirp‑mass precision and 8–20 % η precision are consistent with expectations for SNR ≈ 15–20 events. However, the identified model‑induced biases highlight the need for higher‑order, possibly numerical‑relativity‑calibrated waveforms in future analyses, especially as detector sensitivities improve and higher‑SNR events become routine.

The authors conclude that their methodology is ready for deployment on real detection candidates, offering rapid and reliable astrophysical inference. Future work will extend the pipeline to include eccentricity, higher‑order modes, and a formal treatment of waveform‑model uncertainty within the Bayesian hierarchy, thereby enhancing the robustness of gravitational‑wave astronomy in the advanced detector era.