Unequal arm space-borne gravitational wave detectors

TL;DR

This paper investigates how unequal arm lengths in space-based gravitational wave detectors affect sensitivity, using a noise-canceling method to analyze the impact of arm length ratios on detection capabilities.

Contribution

It extends the analysis of laser noise cancellation techniques to unequal arm configurations, providing insights for the design of space-based detectors like LISA.

Findings

Sensitivity decreases as arm length ratio deviates from unity.

The noise cancellation method remains effective for unequal arms.

Shortening one arm by a factor of 100 significantly impacts sensitivity.

Abstract

Unlike ground-based interferometric gravitational wave detectors, large space-based systems will not be rigid structures. When the end-stations of the laser interferometer are freely flying spacecraft, the armlengths will change due to variations in the spacecraft positions along their orbital trajectories, so the precise equality of the arms that is required in a laboratory interferometer to cancel laser phase noise is not possible. However, using a method discovered by Tinto and Armstrong, a signal can be constructed in which laser phase noise exactly cancels out, even in an unequal arm interferometer. We examine the case where the ratio of the armlengths is a variable parameter, and compute the averaged gravitational wave transfer function as a function of that parameter. Example sensitivity curve calculations are presented for the expected design parameters of the proposed LISA interferometer, comparing it to a similar instrument with one arm shortened by a factor of 100, showing how the ratio of the armlengths will affect the overall sensitivity of the instrument.