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

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 Hz band. At 1 Hz, the strain-equivalent calibration amplitude reaches |hGCal| = 1.16 × 10−14, corresponding to an SNR density of |hGCal|/Sh = 4.16 × 103. 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 δhGCal/hGCal = 0.24%, dominated by geometric alignment uncertainties, while contributions from mass uncertainties and the gravitational constant remain subdominant. The corresponding absolute systematic uncertainty is δhGCal ~ 10−17 at 1 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.