Sky localization of space-based detectors with time-delay interferometry

Abstract: The accurate sky localization of gravitational wave (GW) sources is an important scientific goal for space-based GW detectors. The main differences between future space-based GW detectors, such as Laser Interferometer Space Antenna (LISA), Taiji, and TianQin, include the time-changing orientation of the detector plane, the arm length, the orbital period of the spacecraft and the noise curve. Because of the effects of gravity on three spacecraft, it is impossible to maintain the equality of the arm length, so the time-delay interferometry (TDI) method is needed to cancel out the laser frequency noise for space-based GW detectors. Extending previous work based on equal-arm Michelson interferometer, we explore the impacts of different first-generation TDI combinations and detector's constellations on the sky localization for monochromatic sources. We find that the sky localization power is almost unaffected by the inclusion of the TDI Michelson $(X, Y, Z)$ combination in the analysis. We also find that the variation in the sky localization power for different TDI combinations is entirely driven by the variation in the sensitivities of these combinations. For the six particular TDI combinations studied, the Michelson $(X, Y, Z)$ combination is the best for source localization.