Fuzzy dark matter soliton as gravitational lens
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911416934465536 |
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| author | Wang, Ke Delliou, M. Le |
| author_facet | Wang, Ke Delliou, M. Le |
| contents | The Schrödinger-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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_20323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fuzzy dark matter soliton as gravitational lens Wang, Ke Delliou, M. Le General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics The Schrödinger-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. |
| title | Fuzzy dark matter soliton as gravitational lens |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2507.20323 |