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