Gravitational-wave sensitivity curves

TL;DR

This paper clarifies the multiple conventions used to describe gravitational-wave amplitudes and detector sensitivity, introducing a unified framework that relates characteristic strain $h_c$, PSD-based noise $S_n(f)$, and spectral energy density $S_E(f)$ to the energy-density parameter $ ext{Omega}_{GW}$. It systematically derives the connections among these descriptions, highlights the appropriate contexts for inspirals, stochastic backgrounds, and bursts, and provides practical guidance for generating consistent detector-sensitivity plots. The authors review current and proposed detectors (ground-based, space-based, and PTAs) and summarize representative astrophysical sources across these bands, including fiducial amplitudes and frequency ranges. A key contribution is the demonstration of how to plot and compare sensitivity curves across detectors and sources, aided by online tools, to facilitate cross-disciplinary interpretation and planning for GW astronomy. The work enables clearer, quantitative comparisons essential for planning detections and interpreting future observations in multi-band GW astronomy.

Abstract

There are several common conventions in use by the gravitational-wave community to describe the amplitude of sources and the sensitivity of detectors. These are frequently confused. We outline the merits of and differences between the various quantities used for parameterizing noise curves and characterizing gravitational-wave amplitudes. We conclude by producing plots that consistently compare different detectors. Similar figures can be generated on-line for general use at \url{http://rhcole.com/apps/GWplotter}.

Figures (5)

• Figure 1: The angular response function of an interferometric detector shown both as a surface plot and in an Aitoff--Hammer projection. The quantity that is plotted is is the polarisation average, $\left[(1/2\pi)\int\mathrm{d}\psi \;(F^{+})^{2}+(F^{\times})^{2}\right]^{1/2}$. The response is a function of two sky angles, $\theta$ and $\phi$, and varies between $0$ and $1$. The two detector arms lie in the $x$--$y$ plane either side of one of the zeros in the response.
• Figure 2: The HellingsDowns curve, the correlation between two pulsars separated on the sky by an angle $\theta$.
• Figure 3: A plot of characteristic strain against frequency for a variety of detectors and sources.
• Figure 4: A plot of the square root of power spectral density against frequency for a variety of detectors and sources.
• Figure 5: A plot of the dimensionless energy density in GWs against frequency for a variety of detectors and sources.