Distance measures in gravitational-wave astrophysics and cosmology

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/similar to 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?'

Automated summary

This paper introduces quantities that characterize the sensitivity of gravitational-wave observatories to sources at cosmological distances, including horizon, range, response, and reach distances. These quantities take into account various important effects, such as cosmologically defined distances and volumes, cosmological redshift, cosmological time dilation, and rate density evolution. Unique aspects of gravitational wave detectors, like the variable sky sensitivity and the sensitivity scaling with distance, are also considered.