Orbital effects on time delay interferometry for TianQin

The proposed space-borne laser interferometric gravitational wave (GW) observatory TianQin adopts a geocentric orbit for its nearly equilateral triangular constellation formed by three identical drag-free satellites. The geocentric distance of each satellite is $\approx 1.0 \times 10^{5} ~\mathrm{km}$, which makes the armlengths of the interferometer be $\approx 1.73 \times 10^{5} ~\mathrm{km}$. It is aimed to detect the GWs in $0.1 ~\mathrm{mHz}-1 ~\mathrm{Hz}$. For space-borne detectors, the armlengths are unequal and change continuously which results in that the laser frequency noise is nearly $7-8$ orders of magnitude higher than the secondary noises (such as acceleration noise, optical path noise, etc.). The time delay interferometry (TDI) that synthesizes virtual interferometers from time-delayed one-way frequency measurements has been proposed to suppress the laser frequency noise to the level that is comparable or below the secondary noises. In this work, we evaluate the performance of various data combinations for both first- and second-generation TDI based on the five-year numerically optimized orbits of the TianQin's satellites which exhibit the actual rotating and flexing of the constellation. We find that the time differences of symmetric interference paths of the data combinations are $\sim 10^{-8}$ s for the first-generation TDI and $\sim 10^{-12}$ s for the second-generation TDI, respectively. While the second-generation TDI is guaranteed to be valid for TianQin, the first-generation TDI is possible to be competent for GW signal detection with improved stabilization of the laser frequency noise in the concerned GW frequencies.