Sensitivity functions for space-borne gravitational wave detectors

Time-delay interferometry is put forward to improve the signal-to-noise ratio of space-borne gravitational wave detectors by canceling the large laser phase noise with different combinations of measured data. Based on the Michelson data combination, the sensitivity function of the detector can be obtained by averaging the all-sky wave source positions. At present, there are two main methods to encode gravitational wave signal into detector. One is to adapt gravitational wave polarization angle depending on the arm orientation in the gravitational wave frame, and the other is to divide the gravitational wave signal into plus and cross polarizations in the detector frame. Although there are some attempts using the first method to provide the analytical expression of sensitivity function, only a semianalytical one could be obtained. Here, starting with the second method, we demonstrate the equivalence of both methods. First time to obtain the full analytical expression of sensitivity function, which provides a fast and accurate mean to evaluate and compare the performance of different space-borne detectors, such as LISA and TianQin.

Figure 1

Triangle configuration for space-borne gravitational wave detector. Here, we have adopted the same convention as that in [32].

Figure 2

The GW frame. The signal propagates along $\widehat{w}$ direction, which has the angle ${\theta }_1$ and ${\theta }_2$ with the detector arm 1 and 2, respectively. The detector arms 1 and 2, respectively, locate in the ${\widehat{e}}_X-{\widehat{e}}_Z$ plane, and the angle between the two interference arms is $\gamma$.

Figure 3

The detector frame [53, 54].

Figure 4

The transfer functions for $+$ and $\times$ polarizations are shown as a function of the variable $u$ for all-sky averaged GW sources, when the angle between the two interference arms is $\lambda =\pi /3$. The orange and blue curves represent the averaged antenna GW response functions of plus and cross polarizations, respectively.

Figure 5

Sensitivity curves for the GW detectors (LISA and TianQin) averaging all-sky sources in the four-link configurations.

Figure 6

Dependence of the sensitivity curve of LISA mission for Michelson data combination on the angle between two effective interfering arms ($\gamma =\pi /2$, $\pi /3$ and $\pi /6$).

Figure 7

Sensitivity curve of TianQin mission, which focuses on the GW signal emitted by the special source (J0806). The red line and the pink point represent the mission’s sensitivity curve and the GW signal, respectively.