Letter to the Editor

Direct measurement of the distribution of dark matter with strongly lensed gravitational waves

¹ Department of Astronomy, Beijing Normal University, 100875 Beijing, PR China
e-mail: caoshuo@bnu.edu.cn, zhuzh@bnu.edu.cn
² Advanced Institute of Natural Sciences, Beijing Normal University at Zhuhai, Zhuhai 519087, PR China
³ Department of Physics, College of Sciences, Northeastern University, Shenyang 110004, PR China
⁴ National Centre for Nuclear Research, Pasteura 7, 02-093 Warsaw, Poland
⁵ School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, PR China

Received: 18 November 2021
Accepted: 15 February 2022

Abstract

In this Letter, we present a new idea of probing the distribution of dark matter exhibiting elastic and velocity-independent self-interactions. These interactions might be revealed in multiple measurements of strongly lensed gravitational waves, which can be observationally explored to determine the strength of self-scatterings. Specifically, each individual galactic-scale strong-lensing system whose source is a coalescing compact binary emitting gravitational waves will provide a model-independent measurement of the shear viscosity of dark matter along the line of sight. These individual measurements could be a probe of large-scale distribution of dark matter and its properties. Our results indicate that with 10–1000 strongly lensed gravitational waves from ET and DECIGO, robust constraints on the large-scale distribution of self-interacting dark matter might be produced. More stringent limits on the dark matter scattering cross-section per unit mass (σ_χ/m_χ) relevant to galaxy and cluster scales are also expected, compared with the conservative estimates obtained in the electromagnetic domain. Finally, we discuss the effectiveness of our method in the context of self-interacting dark matter particle physics.