Time-delay interferometry with local delays for TianQin

Time-delay interferometry (TDI) is a postprocessing technique used to suppress the laser phase noise for space-based gravitational wave detectors such as TianQin, by applying specific time-delay combinations to form a virtual equal-armlength interferometer. Recent studies have begun to focus on the onboard delay which is referred to as local delay in this article. Due to the stringent requirement for the laser interferometry in TianQin project, the impact of local delays should be carefully studied. We show the local delays will cause non-negligible effects on TianQin's laser noise reduction, for which we propose two corrections before constructing TDI variables. While the long-arm delay correction has been discussed in previous studies, in this research we also suggest the correction to intermediary variables or original phase measurements. As a proof-of-principle, we present numerical simulation results that coincide with our analytical models, and show that these corrections are valid for different TDI combinations. We find that even if the second-generation TDI is executed perfectly, the residual laser noise is limited by the coupling of local delays and laser locking contents at high frequencies, instead of the previously believed armlength mismatch of the virtual interferometer. Moreover, we disucss the influence of local delays of the test mass interferometer and the reference interferometer, and suggest armlength differences of the two interferometers should be equal for a more effective laser noise elimination. In addition, the traditional expression of ranging bias impact should be rewritten to include additional terms for the local delays and the clock biases. Furthermore, we consider a set of scenarios including six independent lasers and different laser locking configurations, and find the suitable locking schemes for laser noise suppression, which is proved by the simulation results.