Regression of Suspension Violin Modes in KAGRA O3GK Data with Kalman Filters

TL;DR

This work tackles narrowband contamination from suspension violin modes in cryogenic KAGRA data by modeling each mode as a damped oscillator driven by thermal noise and tracking it with a discrete-time Kalman filter. The method uses a rotating-frame, narrowband formulation to estimate the mode envelope in real time and subtract its contribution from the strain channel, aiming to preserve astrophysical signals and the matched-filter SNR. Validation includes reproducing LIGO 40 m noise suppression results and applying the approach to KAGRA O3GK data, where the violin lines are reduced by more than $20$ dB while injected gravitational-wave signals are preserved, as shown by SNR and $\chi^2$ tests. The findings support cleaner strain data for searches and parameter estimation and point toward real-time deployment for upcoming cryogenic detectors like the Einstein Telescope.

Abstract

Suspension thermal modes in interferometric gravitational-wave detectors produce narrow, high-Q spectral lines that can contaminate gravitational searches and bias parameter estimation. In KAGRA, cryogenic mirrors are held by thick suspension fibers, designed to sustain such a low-temperature environment, which may further affect inharmonicity modes, fiber dimensions, and mechanical behavior compared to typical interferometers. As these modes remain a prominent source of narrowband contamination, we implement a Kalman filter to model and track violin lines, building on the methodology introduced in [1], and apply subtraction to KAGRA O3GK data. Using gravitational-wave template injections, we validate that the subtraction preserves matched-filter SNR while effectively suppressing line power. Comparisons of power spectral densities and residual analyses confirm that the method removes deterministic line contributions without introducing waveform distortions. This approach provides a cleaner strain channel for searches and parameter estimation and will become increasingly important for future low-temperature detectors with higher-Q suspensions, such as the Einstein Telescope.

Figures (15)

• Figure 1: Schematic of the KAGRA interferometer 10.1093/ptep/ptaa125. All mirrors with labels are suspended inside the vacuum tanks with four types of vibration isolation systems. The different types of circles in the figure represent the various types of vibration isolation systems. Vacuum tanks in front of the input and end test masses (depicted as dotted grey circles) contain narrow-angle baffles and optical systems for the photon calibrator. ITMX (Y): input test mass X (Y), ETMX (Y): end test mass X (Y), BS: beam splitter, PRM: power recycling mirror, SRM: signal recycling mirror, IMMT (OMMT): input (output) mode-matching telescope, IFI (OFI): input (output) Faraday isolator.
• Figure 2: O3GK strain sensitivity at GPS 1270312960, highlighting the first three violin modes, which are the most prominent suspension thermal noise and the focus of this work.
• Figure 3: Schematic of Type-A suspension 10.1093/ptep/ptaa125. The suspension is a multiple-stage pendulum with a total height of 13m. The Type-A tower is at room temperature, while the cryopayload is cooled to cryogenic temperatures.
• Figure 4: The estimated PSD (GPS 1271267328..1271361536) in the first three violin-mode bands is shown in black, with the fitted Lorentzian profiles overlaid in red. (a) Top: first mode between 170-186Hz ($\Delta f_0 \approx 16$ Hz); (b) Middle: second mode ranging from 402-432Hz ($\Delta f_1 \approx 30$ Hz); (c) Bottom: third modes ranging from 718-770Hz ($\Delta f_2 \approx 52$ Hz)
• Figure 5: The CAD model of the mirror and its suspension wires JoPCS.10.1088. The $x$-axis corresponds to the interferometer’s sensitive direction, while modifications along the $y$ and $z$ axes are effectively shadowed and therefore undetectable.