Shown here is the range of Advanced LIGO and its ability to detect merging black holes. Photo credit: LIGO Collaboration / Amber Stuver / Richard Powell / Atlas of the Universe
The Advanced Laser Interferometer Gravitational Wave Observatory (Advanced LIGO) Detectors and the Virgo detector observed transients directly Gravitational waves (GWs) from compact binary coalescences. After a series of instrument upgrades to further improve sensitivity – such as replacing test masses and optics, increasing laser power and adding compressed light – the two LIGO detectors started the third observation run on April 1, 2019 together with Virgo ( O3) and ended the annual observation on March 27, 2020.
The time series of the dimensionless strain, defined by the different changes in length of the two orthogonal arms divided by the averaged full arm length (~ 4 km in the two LIGO detectors), is used to determine the detection of a GW signal and to deduce the Properties of the astrophysical source. (The figure shows a conceptual diagram of the optical configuration of the Advanced LIGO interferometers.)
Because of the presence of noise and the desire to maintain the resonant state of the optical cavities, the detectors do not measure strain directly. The differential arm displacement is suppressed by the control force assigned to the test masses. The remaining differential arm displacement in the control loop is converted into digitized photodetector output signals. Therefore, the strain is reconstructed from the digitized raw power of each detector with an accurate and precise model of the detector response to the strain. This reconstruction process is known as detector calibration. The accuracy and the accuracy of the estimated detector response and thus the reconstructed strain data are important for the acquisition of GW signals and crucial for the estimation of their astrophysical parameters.
Understanding, accounting for, and / or compensating for the complex valued response of each portion of the updated detectors improves the overall accuracy of the estimated detector response to GWs. The systematic calibration error is the frequency-dependent and time-dependent deviation of the estimated detector response from the actual detector response. We describe our improved understanding and methods of quantifying the response of each detector, striving to define all the places where systematic errors play a role. We use the two LIGO detectors in the first half (six months) of O3 to demonstrate how each identified systematic error affects the reconstructed strain and limits the statistical uncertainty in it. We report the accuracy and precision of the strain data by estimating the 68% confidence interval limits for the systematic error and the uncertainty for the response of each detector (in size and phase).
In the first half of O3, the total systematic error and uncertainty of the best calibrated data in the most sensitive frequency band 20–2000 Hz is within 7% and 4 degrees (?) In phase. The bias in the same band alone is estimated to be less than 2% in size and 2 degrees in phase. The current recording of GW events and the estimation of their astrophysical parameters are not yet limited by such systematic errors and uncertainties. However, as the global GW detector network becomes increasingly sensitive, systematic errors and uncertainties in detector calibration play an increasingly important role. Restrictions due to calibration systematics for estimated GW source parameters, precision astrophysics, population studies, cosmology and tests of general relativity are possible. Efforts are being made to better integrate the work presented in this paper into future GW data analyzes. Research and development of new techniques are ongoing to further reduce systematic errors and uncertainties in calibration below 1%. This is an important milestone to minimize the effects of the calibration system on astrophysical and cosmological results.
Written by Lilli Sun, OzGrav Associate Investigator, ANU
