Kinetic relaxation and Bose-star formation in multicomponent dark matter
Mudit Jain, Mustafa A. Amin, Jonathan P. Thomas, Wisha Wanichwecharungruang
Abstract
Using wave kinetics, we estimate the emergence timescale of gravitating Bose-Einstein condensates/Bose stars in the kinetic regime for a general multicomponent Schr\"odinger-Poisson (SP) system. We identify some effects of the diffusion and friction pieces in the wave-kinetic Boltzmann equation (at leading order in perturbation theory) and provide estimates for the kinetic nucleation rate of condensates. We test our analysis using full ($3+1$)-dimensional simulations of a multicomponent SP system. With an eye toward applications to multicomponent dark matter, we investigate two general cases in detail. First is a massive spin-$s$ field with $N=2s+1$ components (scalar $s=0$, vector $s=1$, and tensor $s=2$). We find that for a democratic population of different components, the condensation timescale is ${\ensuremath{\tau}}_{(s)}\ensuremath{\approx}{\ensuremath{\tau}}_{0}\ifmmode\times\else\texttimes\fi{}N$, where ${\ensuremath{\tau}}_{0}$ is the condensation timescale for the scalar case. Second is the case of two scalars with different boson masses. In this case, we map out how the condensation time depends on the ratios of their average mass densities and boson masses, revealing competition and assistance between components, and a guide toward which component condenses first. For instance, with ${m}_{1}<{m}_{2}$ and not too disparate mass densities, we verify that the timescale of condensation of the first species quickly becomes independent of ${m}_{2}/{m}_{1}$, whereas for equal average number densities, the emergence timescale decreases with increasing ${m}_{2}/{m}_{1}$.