# Binary radial velocity measurements with space-based gravitational-wave detectors

## TL;DR

This paper explores how space-based gravitational-wave detectors like LISA can measure Doppler shifts caused by binary systems orbiting massive black holes, providing new insights into dense astrophysical environments.

## Contribution

It demonstrates the potential of gravitational-wave Doppler shift measurements to probe the environments around black holes, a novel application beyond traditional electromagnetic methods.

## Key findings

- Doppler shifts are potentially detectable by LISA for certain binary configurations.
- Such measurements can reveal properties of the central regions of globular clusters.
- The method extends to studying extragalactic black hole environments.

## Abstract

Unlike traditional electromagnetic measurements, gravitational-wave observations are not affected by crowding and extinction. For this reason, compact object binaries orbiting around a massive black hole can be used as probes of the inner environment of the black hole in regions inaccessible to traditional astronomical measurements. The orbit of the binary's barycenter around the massive black hole will cause a Doppler shift in the gravitational waveform which is in principle measurable by future space-based gravitational-wave interferometers, such as the Laser Interferometer Space Antenna (LISA). We investigate the conditions under which these Doppler shifts are observable by LISA. Our results imply that Doppler shift observations can be used to study the central region of globular clusters in the Milky Way, as well the central environment of extragalactic massive black holes.