Distance measures in gravitational-wave astrophysics and cosmology

TL;DR

This paper introduces and generalizes key distance measures for gravitational-wave detectors, accounting for cosmological effects and detector sensitivities, to better understand their reach in observing distant sources.

Contribution

It presents new generalized distance metrics for gravitational-wave observatories that incorporate cosmological effects and detector characteristics.

Findings

Defined and generalized horizon, range, response, and reach distances.

Provided online tools for calculating gravitational-wave distances.

Clarified how far gravitational-wave detectors can observe distant sources.

Abstract

We present quantities which characterize the sensitivity of gravitational-wave observatories to sources at cosmological distances. In particular, we introduce and generalize the horizon, range, response, and reach distances. These quantities incorporate a number of important effects, including cosmologically well-defined distances and volumes, cosmological redshift, cosmological time dilation, and rate density evolution. In addition, these quantities incorporate unique aspects of gravitational wave detectors, such as the variable sky sensitivity of the detectors and the scaling of the sensitivity with inverse distance. An online calculator (https://users.rcc.uchicago.edu/~dholz/gwc/) and python notebook (https://github.com/hsinyuc/distancetool) to determine GW distances are available. We provide answers to the question: "How far can gravitational-wave detectors hear?"