[Paper Review] Characterization of systematic error in Advanced LIGO calibration in the second half of O3

L. Sun, E. Goetz+20 more|arXiv (Cornell University)|Jun 30, 2021

Pulsars and Gravitational Waves ResearchPhysics and Astronomy1 references18 citations

TL;DR

This paper characterizes systematic calibration errors in Advanced LIGO's strain reconstruction during the second half of O3 (O3B), finding that frequency-dependent response function modeling dominates uncertainty. The upper limit on systematic error is 11.29% in magnitude and 9.18° in phase (68% CI) in the 20–2000 Hz band, with the dominant source being imperfect modeling of detector response frequency dependence rather than absolute calibration reference uncertainty.

ABSTRACT

We present the probability distribution of the systematic errors in the most accurate, high-latency version of the reconstructed dimensionless strain $h$, at the Hanford and Livingston LIGO detectors, used for gravitational-wave astrophysical analysis, including parameter estimation, in the last five months of the third observing run (O3B). This work extends the results presented in Sun et. al (2020) [1] for the first six months of the third observing run (O3A). The complex-valued, frequency-dependent, and slowly time-varying systematic error (excursion from unity magnitude and zero phase) in O3B generally remains at a consistent level as in O3A, yet changes of detector configurations in O3B have introduced a non-negligible change in the frequency dependence of the error, leading to larger excursions from unity at some frequencies and/or during some observational periods; in some other periods the excursions are smaller than those in O3A. For O3B, the upper limit on the systematic error and associated uncertainty is 11.29% in magnitude and 9.18 deg in phase (68% confidence interval) in the most sensitive frequency band 20-2000 Hz. The systematic error alone is estimated at levels of < 2% in magnitude and $\lesssim 4$ deg in phase. These errors and uncertainties are dominated by the imperfect modeling of the frequency dependence of the detector response functions rather than the uncertainty in the absolute reference, the photon calibrators.

Motivation & Objective

• To quantify systematic errors in the high-latency strain reconstruction of Advanced LIGO during O3B, the second half of the third observing run.
• To assess how changes in detector configurations during O3B affected the frequency dependence and time evolution of calibration errors compared to O3A.
• To determine the dominant sources of uncertainty in the calibration response function model, particularly relative to the absolute photon calibrator reference.
• To provide updated error bounds for use in gravitational-wave astrophysical parameter estimation, especially for high signal-to-noise ratio events.
• To support future studies on calibration error impacts on cosmology and tests of General Relativity using multi-epoch event catalogs.

Proposed method

• Uses a parameterized control system model to reconstruct the dimensionless strain $ h $, based on error signals $ d_{\text{err}} $, digital filters $ D $, and modeled actuation $ A^{\text{model}} $ and sensing functions $ C^{\text{model}} $.
• Defines the modeled response function $ R^{\text{model}} = \frac{1 + A^{\text{model}} D C^{\text{model}}}{C^{\text{model}}} $, which maps error signals to strain estimates.
• Quantifies systematic error via $ \eta_R = \frac{R}{R^{\text{model}}} $, where $ R $ is the true response function, and analyzes its complex-valued, frequency-dependent, and time-varying deviations from unity.
• Employs a Bayesian framework to estimate the probability distribution of $ \eta_R $, incorporating uncertainties from detector response modeling and calibration reference stability.
• Compares error characteristics between O3A and O3B, identifying shifts in frequency dependence due to hardware and configuration changes.
• Decomposes total uncertainty into contributions from individual frequency-dependent components of the response function model and the absolute calibration reference (photon calibrators).

Experimental results

Research questions

• RQ1 How do systematic calibration errors in Advanced LIGO’s strain reconstruction during O3B compare in magnitude and frequency dependence to those in O3A?
• RQ2 What is the dominant source of uncertainty in the calibration response function model—modeling of frequency-dependent terms or uncertainty in the absolute photon calibrator reference?
• RQ3 How do configuration changes in O3B affect the time evolution and spectral shape of systematic calibration errors?
• RQ4 What are the upper bounds on systematic error in magnitude and phase for the most sensitive frequency band (20–2000 Hz) during O3B?
• RQ5 To what extent are current calibration errors negligible for astrophysical parameter estimation, especially for high signal-to-noise ratio events?

Key findings

• The systematic error in the most sensitive frequency band (20–2000 Hz) during O3B is bounded at 11.29% in magnitude and 9.18° in phase at the 68% credible interval.
• The systematic error alone is estimated at less than 2% in magnitude and less than 4° in phase, indicating that the dominant uncertainty arises from modeling the frequency dependence of the detector response.
• Despite improvements in absolute calibration reference (photon calibrators), their uncertainty remains subdominant compared to errors in modeling the frequency-dependent components of the response function.
• The frequency dependence of systematic errors changed in O3B due to detector configuration upgrades, leading to larger excursions at certain frequencies or during specific periods compared to O3A.
• In some observational periods during O3B, systematic errors were smaller than in O3A, highlighting non-stationary behavior in calibration error characteristics.
• The results confirm that calibration errors at current levels are not a limiting factor for transient gravitational wave detection but remain a critical consideration for high-precision astrophysical parameter estimation and cosmological studies.