Fuzzy dark matter soliton as gravitational lens

TL;DR

This paper investigates how fuzzy dark matter solitons could gravitationally lens gravitational waves, finding that the effect is very small and currently undetectable by pulsar timing arrays.

Contribution

The study provides the first numerical simulation of gravitational lensing effects of FDM solitons on gravitational waves, revealing the magnitude and scale of the antisotropy in the GW background.

Findings

Maximum GW magnification factor is about 10^{-4}.

Magnification zone extends approximately 6 parsecs.

Antisotropy in GW background is around 10^{-4}, below current detection sensitivity.

Abstract

The Schr\"odinger-Poisson (SP) equations predict fuzzy dark matter (FDM) solitons. Given the FDM mass $\sim10^{-20}\rm~{eV}/c^2$, the FDM soliton in the Milky Way is massive $\sim 10^7~M_{\odot}$ but diffuse $\sim 10{\rm~pc}$. Therefore, such FDM soliton can serve as a gravitational lens for gravitational waves (GWs) with frequency $\sim10^{-8}{\rm~Hz}$. In this paper, we investigate its gravitational lensing effects by numerical simulation of the propagation of GWs through it. We find that the maximum magnification factor of GWs is very small $\sim10^{-4}$, but the corresponding magnification zone is huge $\sim6{\rm~pc}$ for FDM with mass equal to $8\times10^{-21}\rm~{eV}/c^2$. Consequently, this small magnification factor compounding over such large magnification zone results in a small antisotropy of $\sim10^{-4}$ over a large solid angle in the GW background. That level of antisotropy is out of the sensitivity, $<20\%$, of the pulsar timing arrays today.