Evaluating residual acceleration noise for the TianQin gravitational waves observatory with an empirical magnetic field model

TianQin (TQ) project plans to deploy three satellites in space around the Earth to measure the displacement change of test masses caused by gravitational waves via laser interferometry. The requirement of the acceleration noise of the test mass is on the order of 10(-15) m s(-2 )Hz(-1/2) in the sensitive frequency range of TQ, which is so stringent that the acceleration noise caused by the interaction of the space magnetic field with the test mass needs to be investigated. In this work, by using the Tsyganenko model, a data-based empirical space magnetic field model, we obtain the magnetic field distribution around TQ's orbit spanning two solar cycles in 23 years from 1998 to 2020. With the obtained space magnetic field, we derive the distribution and amplitude spectral densities of the acceleration noise of TQ in 23 years. Our results reveal that the average values of the ratio of the acceleration noise caused by the space magnetic field to the requirements of TQ at 1 mHz (R-1 mHz) and 6 mHz (R-6 mHz) are 0.123 +/- 0.052 and 0.027 +/- 0.013, respectively. The occurrence probabilities of R-1 mHz > 0.2 and > 0.3 are only 7.9% and 1.2%, respectively, and R-6 mHz never exceeds 0.2.