Sensitivity curves for spaceborne gravitational wave interferometers

TL;DR

This paper details the computation of sensitivity curves for spaceborne gravitational wave detectors, correcting prior errors and providing the first mostly analytic transfer function, with implications for the LISA observatory.

Contribution

It introduces a detailed method for calculating sensitivity curves, corrects previous inaccuracies, and presents the first mostly analytic transfer function for spaceborne gravitational wave detectors.

Findings

Previous LISA sensitivity was underestimated by a factor of √3.

Provides the first mostly analytic gravitational wave transfer function.

Offers example sensitivity curves for the proposed LISA detector.

Abstract

To determine whether particular sources of gravitational radiation will be detectable by a specific gravitational wave detector, it is necessary to know the sensitivity limits of the instrument. These instrumental sensitivities are often depicted (after averaging over source position and polarization) by graphing the minimal values of the gravitational wave amplitude detectable by the instrument versus the frequency of the gravitational wave. This paper describes in detail how to compute such a sensitivity curve given a set of specifications for a spaceborne laser interferometer gravitational wave observatory. Minor errors in the prior literature are corrected, and the first (mostly) analytic calculation of the gravitational wave transfer function is presented. Example sensitivity curve calculations are presented for the proposed LISA interferometer. We find that previous treatments of LISA have underestimated its sensitivity by a factor of $\sqrt{3}$.