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arXiv · 2507.20323

Fuzzy dark matter soliton as gravitational lens

Ke Wang·M. Le Delliou
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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.

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Ke Wang, M. Le Delliou. 2025-07-27. Fuzzy dark matter soliton as gravitational lens. https://arxiv.org/abs/2507.20323

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