Gravitational Waves from Post-Collision of Fuzzy Dark Matter Solitons

According to the Schr\"odinger-Poisson (SP) equations, fuzzy dark matter (FDM) can form a stable equilibrium configuration, the so-called FDM soliton. The SP system can also determine the evolution of FDM solitons, such as head-on collision. In this paper, we first propose a new adimensional unit of length, time and mass. And then, we simulate the adimensional SP system with $\mathtt{PyUltraLight}$ to study the GWs from post-collision of FDM solitons when the linearized theory is valid and the GW back reaction on the evolution of FDM solitons is ignored. Finally, we find that the GWs from post-collisions have a frequency of (few ten-years)$^{-1}$ or (few years)$^{-1}$ when FDM mass is $m=10^{-18}\rm{eV}/c^2$ or $m=10^{-17}\rm{eV}/c^2$. Therefore, future detection of such GWs will constrain the property of FDM particle and solitons.