Kinetic relaxation and nucleation of Bose stars in self-interacting wave dark matter

Abstract

We revisit kinetic relaxation and soliton/Boson star nucleation in fuzzy scalar dark matter featuring short-ranged self-interactions ${\mathcal{H}}_{\mathrm{int}}=-\lambda |\psi {|}^4/2m^2$, alongside gravitational self-interactions. We map out the full curve of nucleation timescale for both repulsive ($\lambda <0$) and attractive ($\lambda >0$) short-ranged self-interaction strength, and in doing so reveal two new points. Firstly, besides the two usual terms, $\propto G^2$ and $\propto {\lambda }^2$, in the total relaxation rate ${\Gamma }_{\mathrm{relax}}$, there is an additional cross term $\propto G\lambda$ arising due to interference between gravitational and short-ranged self-interaction scattering amplitudes. This yields a critical repulsive interaction strength ${\lambda }_{\mathrm{cr}}\simeq -2\pi G{m}^2/v_0^2$, at which the relaxation rate is smallest and serves as the transition point between typical net attractive self-interaction ($\lambda \gtrsim {\lambda }_{\mathrm{cr}}$), and net repulsive self-interaction ($-\lambda \gtrsim -{\lambda }_{\mathrm{cr}}$). Secondly, while in the net attractive regime, nucleation time scale is similar to inverse relaxation time scale ${\tau }_{\mathrm{nuc}}\sim {\Gamma }_{\mathrm{relax}}^{-1}$, in the net repulsive regime nucleation occurs at a delayed time ${\tau }_{\mathrm{nuc}}\sim (\lambda /{\lambda }_{\mathrm{cr}}){\Gamma }_{\mathrm{relax}}^{-1}$. We confirm our analytical understanding by performing 3D field simulations with varying average mass density $\bar{\rho }$, box size $L$ and grid size $N$.

11 pages, 5 figures, 2 appendices

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