⚛️ general relativity

Calibration of the AdvancedVirgo+ Gravitational Wave Detector and Reconstruction of the Detector Strain h(t) during the Observing Run O4

This paper details the calibration methods, online strain reconstruction, and offline uncertainty estimation for the Advanced Virgo+ detector during the O4 observing run, highlighting its critical role in improving source localization despite limited sensitivity and confirming the data's availability for public scientific analysis.

Original authors: Virgo Collaboration

Published 2026-07-22

📖 3 min read🧠 Deep dive

CC BY 4.0

Original authors: Virgo Collaboration

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, invisible ocean. Most of the time, this ocean is calm, but occasionally, massive events—like two black holes crashing into each other or neutron stars colliding—create ripples that travel across space and time. These ripples are called gravitational waves. They are so faint that by the time they reach Earth, they are stretching and squeezing our planet by a distance smaller than the width of a single atom. To catch these whispers from the cosmos, scientists built giant, ultra-sensitive ears called interferometers. These machines use lasers and mirrors to measure tiny changes in distance. However, because the signals are so incredibly weak, the "ears" themselves can be noisy or slightly out of tune. If the instrument isn't perfectly calibrated—if we don't know exactly how much a signal on the screen corresponds to a real stretch in space—we might mistake a glitch for a cosmic event, or worse, miss a real event entirely. This is why "calibration" is the unsung hero of gravitational wave astronomy: it's the process of tuning the instrument so that the data we collect is a true, honest reflection of the universe's ripples.

This paper is the official report card for the "Advanced Virgo+" detector, a massive gravitational wave observatory located near Pisa, Italy, during its fourth major listening period, known as "O4," which ran from April 2024 to November 2025. The authors, a huge team of scientists from the Virgo Collaboration, explain exactly how they tuned their instrument to hear these cosmic whispers clearly. Think of the detector as a giant, high-tech drum. When a gravitational wave hits, it changes the drum's shape. But the drum is also being shaken by the wind, the ground, and its own internal electronics. To figure out which vibration came from space and which came from a passing truck, the team had to build a perfect map of how the drum responds to every possible shake. They used special "reference actuators"—devices that push the mirrors with known, precise forces, like a tiny, invisible finger tapping the drum to see how it rings. By comparing the known tap to the recorded sound, they could build a correction map.

The paper details how they used two main tools for this tuning: "Photon Calibrators" (which use laser light pressure to push the mirrors) and "Newtonian Calibrators" (which use spinning weights to create a tiny, changing gravitational pull). For the first time, they used the Newtonian Calibrators as their primary ruler, finding them to be incredibly stable and accurate. They discovered that their instrument was so well-tuned that the "noise" they had to subtract was minimal, and the final data they produced (called "Analysis Ready" data) had a residual error of less than 1% in strength and a timing error of just a few microseconds. They also found that while the detector was generally very steady, there were specific frequencies (around 50 Hz and 150 Hz, which are related to the electrical power grid) where the noise was too high to trust the data, so they marked those spots as "do not use." The result is a set of ultra-clean, highly accurate data files that other scientists can use to study the black holes and neutron stars that created the waves, confident that the measurements are as true to reality as human engineering can make them.

Technical Summary: Calibration of the AdvancedVirgo+ Gravitational Wave Detector and Reconstruction of the Detector Strain h(t) during the Observing Run O4

Problem and Context
The AdvancedVirgo+ detector participated in the LIGO-Virgo-KAGRA (LVK) O4 observing run (specifically periods O4b and O4c, from April 2024 to November 2025). While the detector achieved a binary neutron star (BNS) range of approximately 55 Mpc, its inclusion in the network was critical for improving the sky localization of gravitational wave (GW) sources. To utilize the data for parameter estimation and source localization, the detector strain $h(t)$ must be reconstructed with high precision. The primary challenge is to convert the raw interferometer output (power variations at the dark fringe) and control signals into a dimensionless strain time series that accurately reflects the differential arm-length variations induced by passing GWs. This requires precise calibration of the sensing chain (photodiodes), the actuation system (electromagnetic coils on mirrors and marionettes), and the optical response of the interferometer, all while accounting for systematic biases and frequency-dependent uncertainties.

Methodology
The paper details the calibration and reconstruction pipeline used during O4, building upon methods established in O2 and O3 but introducing specific refinements:

Reference Actuators: The calibration hierarchy was updated. For the first time, the Newtonian Calibrator (Ncal), which induces a variable gravity field using rotating masses, served as the primary length reference below a few tens of Hertz, achieving a systematic uncertainty of 0.12%. The Photon Calibrators (Pcal), which use radiation pressure from auxiliary lasers, were calibrated against the Ncal (reducing their uncertainty to 0.48%) and subsequently used to calibrate the mirror electromagnetic actuators across the 10 Hz to 2 kHz band.
Actuator and Sensing Calibration:
- Photodiodes: The output photodiode sensing chain was modeled as an 8th-order low-pass Butterworth filter with a pure delay. The chain was recalibrated following hardware changes in September 2023 and September 2025.
- Actuators: Mirror and marionette electromagnetic actuators were calibrated by comparing their response to the Pcal reference. This involved measuring transfer functions for the North-East (NE), West (WE), North-West (NW), and Beam Splitter (BS) mirrors and their associated marionettes.
- Timing: Absolute timing precision was maintained at the $\sim 1 \mu s$ level for the photodiode readout and $\sim 3 \mu s$ for the mirror actuators.
Strain Reconstruction ( $h(t)$ ):
- The reconstruction occurs in the frequency domain using Fast Fourier Transforms (FFTs) over 8-second windows with 4-second overlap.
- The raw strain ( $h_{raw}$ ) is computed by subtracting the contributions of control signals (applied to maintain cavity resonance) from the calibrated dark-fringe power signal.
- Unbiasing: A new feature for O4 involved the online correction of frequency-dependent biases in $h_{raw}$ . A bias model, derived from offline analysis of calibration injections, was applied to produce an unbiased strain ( $h_{unbias}$ ).
- Noise Subtraction: Linear noise subtraction was applied to remove noise coupled from known sources (e.g., Michelson control noise and Signal Recycling control noise) using witness channels.
Monitoring and Validation:
- Permanent sine-wave injections (calibration lines) at specific frequencies (e.g., ~36 Hz, ~70 Hz, ~360 Hz) were continuously injected to monitor optical gains, cavity poles, and actuator stability.
- Dedicated weekly injections of 27 lines and broadband noise injections were used to measure the bias of the reconstructed strain.
- The "Analysis Ready" (AR) dataset was produced offline, incorporating updated uncertainty estimates and bias corrections not available in the low-latency online stream.

Key Contributions and Results

Calibration Precision: The mirror actuator models achieved a total uncertainty of 0.77% in modulus and 3 mrad in phase (valid from 10 Hz to 1.5 kHz). Marionette actuator uncertainties were higher (up to 5.1% in modulus) but sufficient for their lower frequency control range.
Bias Correction: The online unbiasing procedure successfully corrected the raw strain bias. The residual bias of the final $h(t)$ time series was negligible, remaining below 0.5% in modulus and 10 mrad in phase across most of the band.
Uncertainty Quantification: The paper provides the first frequency-dependent uncertainty estimates for the Virgo $h(t)$ $h (t)$ data. The typical uncertainty is ~2.5% in modulus and <40 mrad in phase (rising at high frequencies due to timing uncertainties).
- Note: Uncertainties are significantly larger around 50 Hz and 150 Hz (up to 20% in amplitude) due to mains noise contamination, though these bands are typically excluded from parameter estimation analyses.
Timing Accuracy: The absolute timing precision is estimated at 1 $\mu$ s for the photodiode readout and 3 $\mu$ s for the mirror actuators, meeting the requirement of better than 0.01 ms for source localization.
Data Products: Two datasets were produced:
1. Online Strain: Distributed with ~10 s latency for low-latency searches and alerts.
2. Analysis Ready (AR) Strain: Released offline with updated bias corrections and frequency-dependent uncertainties, made available via the Gravitational Wave Open Science Center (GWOSC).

Significance and Claims
The paper asserts that the calibration and reconstruction methods described enabled the AdvancedVirgo+ detector to contribute effectively to the O4 observing run. Key claims regarding the significance of this work include:

Improved Source Localization: Despite the detector's limited sensitivity range (~55 Mpc), its inclusion in the network improved the accuracy of source parameter estimation, particularly sky localization.
Bias Mitigation: The implementation of online bias correction ensures that low-latency searches for compact binary coalescences do not suffer from efficiency losses due to calibration errors, a critical improvement for future high-SNR detections.
Standardization: The provision of frequency-dependent uncertainty estimates allows for more rigorous statistical analysis of GW events. The paper notes that while the Virgo convention for reporting uncertainties ( $h_{rec}/h_{true}$ ) differs from LIGO and KAGRA, this information is fully documented to facilitate joint analyses.
Validation: The stability of the calibration models throughout the run, verified by continuous monitoring and periodic injections, confirms that the systematic uncertainties are well-characterized and within the requirements set for the O4 run.

The authors conclude that the Virgo AR frame files, containing the final calibrated strain and associated uncertainties, were successfully used for the scientific analyses and publications resulting from the O4b and O4c runs.

More like this