Impact of combinations of time-delay interferometry channels on stochastic gravitational wave background detection

TL;DR

This paper derives the exact overlap reduction function for A/E channels in TDI, improving the accuracy of stochastic gravitational wave background detection sensitivity estimates for space-based detectors like TianQin and LISA.

Contribution

It provides the exact form of the overlap reduction function for A/E channels, addressing limitations of the low-frequency approximation.

Findings

Sensitivity curves for TianQin, TianQin I+II, and TianQin + LISA were calculated.

Detection sensitivity with A/E channels aligns with that from equal-arm Michelson channels.

Exact overlap reduction function enhances accuracy in stochastic background detection estimates.

Abstract

The method of time delay interferometry (TDI) is proposed to cancel the laser noise in space-borne gravitational-wave detectors. Among all different TDI combinations, the most commonly used ones are the orthogonal channels A, E and T, where A and E are signal-sensitive and T is signal-insensitive. Meanwhile, for the detection of stochastic gravitational-wave background, one needs to introduce the overlap reduction function to characterize the correlation between channels. For the calculation of overlap reduction function, it is often convenient to work in the low-frequency approximation, and assuming the equal-arm Michelson channels. However, if one wishes to work on the overlap reduction function of $\rm A/E$ channels, then the low-frequency approximation fails. We derive the exact form of overlap reduction function for $\rm A/E$ channels. Based on the overlap reduction function, we calculate the sensitivity curves of TianQin, TianQin I+II and TianQin + LISA. We conclude that the detection sensitivity calculated with $\rm A/E$ channels is mostly consistent with that obtained from the equal-arm Michelson channels.