Sensitivity functions for space-borne gravitational wave detectors

TL;DR

This paper derives a comprehensive analytical expression for the sensitivity function of space-borne gravitational wave detectors, enabling efficient performance evaluation and comparison of detectors like LISA and TianQin.

Contribution

It demonstrates the equivalence of two methods for encoding gravitational wave signals and provides the first full analytical sensitivity function expression for space-borne detectors.

Findings

Derived the full analytical sensitivity function expression.

Established the equivalence of two encoding methods.

Facilitated rapid performance evaluation of detectors.

Abstract

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.