Kinetic relaxation and Bose-star formation in multicomponent dark matter

Mudit Jain, Mustafa A. Amin, Jonathan Thomas, and Wisha Wanichwecharungruang

Phys. Rev. D 108, 043535 – Published 28 August 2023

Abstract

Using wave kinetics, we estimate the emergence timescale of gravitating Bose-Einstein condensates/Bose stars in the kinetic regime for a general multicomponent Schrödinger-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 $N = 2 s + 1$ 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 $τ_{(s)} \approx τ_{0} \times N$ , where $τ_{0}$ 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 $m_{2} / m_{1}$ .

Received 22 May 2023
Accepted 7 August 2023

DOI:https://doi.org/10.1103/PhysRevD.108.043535

Physics Subject Headings (PhySH)

Bosonization Classical solutions in field theory Cosmology Dark matter Growth processes Kinetic theory Localization Nonequilibrium statistical mechanics Nonperturbative effects in field theory Nucleation Particle dark matter Pattern formation Phase transitions Statistical field theory

Fokker–Planck equation

Particles & FieldsGravitation, Cosmology & AstrophysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Mudit Jain ^*, Mustafa A. Amin^†, Jonathan Thomas ^‡, and Wisha Wanichwecharungruang^§

Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA

^*mudit.jain@rice.edu
^†mustafa.a.amin@rice.edu
^‡jt57@rice.edu
^§wisha@rice.edu

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Issue

Vol. 108, Iss. 4 — 15 August 2023

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Images

Figure 1
Top panel: Maximum density in the simulation volume as a function of time for scalar ( $s = 0$ ), vector ( $s = 1$ ), and tensor fields ( $s = 2$ ). The condensation time scales with the number of components of the field as $τ_{(s)} \sim τ_{0} \times N$ , where $N = 2 s + 1$ . The simulated data include 14 simulations for $s = 0$ , 1, 2 each. For visual clarity, the outputs shown are significantly undersampled compared to what is available from our simulations. Lower panels: In each row (corresponding to scalar, vector, and tensor fields, respectively), the first two panels show a projection of the mass density of the spin- $s$ field at initial and final times, while the third panel provides the radial profile of the mass density (the solid line is the expected soliton profile) at the final time. Some simulation animations are available in the Supplemental Material [24].
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Figure 2
The simulation snapshots in the top and bottom rows show the initial and final projections of the magnitude of the spin density for vector and tensor cases, respectively. The rightmost column shows the radial profile of the magnitude of the spin density at the final time. Note that spin accumulates with the density (compare with the bottom two rows of Fig. 1). Restoring factors of $ℏ$ , the spin per boson in the simulation volume is $O (10^{- 2}) ℏ$ , whereas in the core it concentrates to $O (1) ℏ$ . Unlike the magnitude of the radial spin density profile, spin in the core and in the simulation volume is obtained by vector summation of spin density at each location.
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Figure 3
Two-component simulations with equal mass density in each component, but different boson masses. The boson mass and mass density of the first component are held fixed. Top panel: Maximum density of each component of the field as a function of time in the simulation volume. Three simulations are shown, each with a different ratio of boson masses between the two components. The transparent version of each color corresponds to the heavier component. Note that there is no significant dependence of the condensation time on the mass ratios considered here. Also note the slower accumulation rate at late times for the heavier component. Bottom panel: The first two panels show the final projected densities in the lighter and heavier components, whereas the third panel shows their radial profiles. The heavier component is accumulating around the condensed lighter one. Some simulation animations are available in the Supplemental Material [24].
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Figure 4
Two-component simulations with equal number density in each component, but different boson masses. The boson mass and mass density of the first component are held fixed. Top panel: Two simulations are shown, each with a different ratio of boson masses between the two components. The transparent version of each color corresponds to the heavier component. In contrast with the equal mass density case, the condensation time decreases with increasing $m_{2} / m_{1}$ . Bottom panel: The first two panels show final projected densities in the lighter and heavier components, whereas the third panel shows their radial profiles. Note that the difference in initial mass densities between the two components is still visible at large radii from the soliton’s center.
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Figure 5
Left panel: Analytical estimate for the timescale of emergence in two component systems with different boson masses and average mass densities, based on the initial kinetic relaxation rate Eq. (10). To the right of the dotted line, the component with boson mass $m_{1}$ condenses first, whereas to the left of the dotted line, the component with boson mass $m_{2}$ condenses first. Times are normalized by the equal-density, equal-boson-mass case. We vary $m_{2}$ and ${\bar{ρ}}_{2}$ , keeping $m_{1}$ and ${\bar{ρ}}_{1}$ fixed. Right table/panel: Condensation times (normalized by $τ_{1, 1}$ for each simulation set) extracted from numerical simulations. For each ${{\bar{ρ}}_{2} / {\bar{ρ}}_{1}, m_{2} / m_{1}}$ point, we have averaged over five simulation runs with two different values of ${\bar{ρ}}_{1}$ . The qualitative trends with density and mass ratios match the theoretical expectations.
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