Improving calibration accuracy with torque coupled gravity field calibrator for sub-Hz gravitational wave observation in CHRONOS

Abstract

A fundamental challenge in low-frequency gravitational-wave detectors is the limited signal-to-noise ratio (SNR) of calibration lines, particularly in torsion-bar systems where the response is governed by rotational dynamics. In this work, we resolve this issue by optimizing the geometrical configuration of a torque-coupled gravity field calibrator (GCal), achieving an improvement in calibration-line SNR by more than an order of magnitude compared to conventional layouts. For the Cryogenic sub-Hz cROss torsion-bar detector with quantum NOn-demolition Speed-meter (CHRONOS), the calibration signal appears as a monochromatic line within the $0.1$--$10~\mathrm{Hz}$ band. At $1~\mathrm{Hz}$, the strain-equivalent calibration amplitude reaches $|h_{\rm GCal}| = 1.18 \times 10^{-14}$, corresponding to an SNR density of $|h_{\rm GCal}|/S_h = 4.25 \times 10^{3}$. This demonstrates for the first time that a high-SNR calibration line can be directly injected into the sub-Hz band of a torsion-bar detector. A first-order perturbative error propagation analysis yields a total fractional systematic uncertainty of $\delta h_{\rm GCal}/h_{\rm GCal} = 0.24\%$, dominated by geometric alignment uncertainties, while contributions from mass uncertainties and the gravitational constant remain subdominant. The corresponding absolute systematic uncertainty is $\delta h_{\rm GCal} \sim 10^{-17}$ at $1~\mathrm{Hz}$. These results establish torque-coupled gravitational calibration as a practical solution to the longstanding low-SNR problem in sub-Hz torsion-bar detectors and provide a robust pathway toward precision absolute calibration in the low-frequency regime.