Sensitivity functions of space-borne gravitational wave detectors under the metric gravity theory

Gravitational waves (GWs) have six possible polarization modes, and whose successful detection can effectively test the gravitational properties under the strong field theory and help distinguish between different theories of gravity. Space-based GW detectors can respond differently to different polarization modes and can be used to measure the polarization states of GWs. However, during the detection process, multiple noises can swamp the faint GW signals, thus, it is essential to develop highly sophisticated experimental techniques and data processing methods to suppress the noises. For the most dominant laser frequency noise, time-delay interferometry technique is employed to construct a virtual equal-arm interferometer by performing appropriate time-delay and linear combination of data streams. This ensures the laser frequency noise is suppressed below the noise floor composed of test-mass noise and shot noise. To present the responsiveness of the detector to the polarization modes of GW signals and to clarify the corresponding characteristic regularities. In this paper, we calculate and analyze the sensitivity functions of 45 core geometric time-delay interferometry technique (TDI) combinations under the six polarization modes allowed by the metric gravity theory. The analysis is based on arbitrary second-generation TDI that can be independently linearly expanded by first-generation generators. It turns out that the sensitivity functions of 45 TDI combinations in different polarization modes are classified into exactly the same 11 categories, and there are obvious characteristic patterns in the asymptotic behavior of these sensitivity functions. These results can help to measure the GW polarization states, understand the nature of fields beyond the gravitational field, and provide some support for distinguishing gravitational theories. In addition, the sensitivity functions of multi-type TDI combinations can be applied to the parameter estimation to improve the localization accuracy of all-sky GW sources.