Estimate of magnetic stiffness noise in space-based gravitational wave detection

Abstract Magnetic noises play a key role in the instrument sensitivity in the low frequency regime, which corresponds to the measurement band of interest for future space-based gravitational wave detection. The magnetic noises can be divided into those that are time variant, but independent of test mass position (direct terms) and those that are time invariant, but a function of position (stiffness terms). The direct terms have been analyzed through the LISA Pathfinder on-orbit magnetic experiments (Armano et al 2025 Phys. Rev. Lett. 134 071401), while the stiffness terms have not been estimated in depth. In this paper, we present an estimate of the magnetic stiffness contribution to the instrument performance based on typical parameters of the test mass magnetic properties and the local magnetic field environment. Our results show that, if the relative motion between the TianQin spacecraft and the test mass can reach the designed level of 3 nm Hz − 1 / 2 , the residual acceleration due to magnetic stiffness noise is at the level of 1 × 10 − 17 m s − 2 Hz − 1 / 2 . Under these conditions, magnetic stiffness noise is not significant for the TianQin mission.