Fuzzy dark matter soliton as gravitational lens

Abstract

The Schrödinger-Poisson (SP) equations predict fuzzy dark matter (FDM) solitons. Given the FDM mass $\sim 10^{-20}\mathrm{eV}/{\mathrm{c}}^2$, the FDM soliton in the Milky Way is massive $\sim 10^7{M}_{\odot }$ but diffuse $\sim 10\mathrm{pc}$. Therefore, such FDM soliton can serve as a gravitational lens for gravitational waves (GWs) with frequency $\sim 10^{-8}\mathrm{Hz}$. 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 $\sim 10^{-4}$, but the corresponding magnification zone is huge $\sim 6\mathrm{pc}$ for FDM with mass equal to $8\times 10^{-21}\mathrm{eV}/{\mathrm{c}}^2$. Consequently, this small magnification factor compounding over such large magnification zone results in a small antisotropy of $\sim 10^{-4}$ 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.

10 pages, 5 figures