Ultra-Strongly Self-Interacting Dark Matter: From Phenomenology to Astrophysical Observables

TL;DR

This work proposes a minimal two-component self-interacting dark matter model in which a dominant SIDM species coexists with a subpercent ultra-strongly self-interacting component (uSIDM) mediated by a light dark photon. The authors derive analytic relic-density relations by solving coupled Boltzmann equations, showing the interconversion χ1χ1→χ2χ2 is suppressed and does not spoil the χ1 freeze-out, and map the microphysics to ETHOS parameters to compute the linear matter power spectrum with CLASS. Astrophysical constraints from dwarf galaxies, low-surface-brightness systems, and strong-lensing clusters delineate a viable window in the mediator-to-DM mass ratio m_{A'}/m_χ and the uSIDM coupling α_{χ2}, while direct-detection limits with kinetic mixing ε_γ further restrict parameter space. They find a region where σ_eff/m ≈ 20–40 cm^2/g at dwarf velocities and σ_eff/m < 0.13 cm^2/g at cluster scales, with a subpercent uSIDM fraction providing seeds for early black-hole formation and a small-scale power spectrum consistent with current data but bearing potentially observable non-standard features at future experiments. Overall, the model is cosmologically viable and testable, offering a concrete link between microphysics, halo phenomenology, and structure formation with a clearly delineated viable region.

Abstract

We develop a minimal, testable framework for two-component self-interacting dark matter (SIDM) in which a dominant, moderately self-interacting species coexists with an ultra-strongly self-interacting subcomponent (uSIDM). A light vector mediator induces velocity-dependent self-scattering, while early-universe dynamics - standard $2 \to 2$ annihilation supplemented by interconversion $χ_1χ_1 \to χ_2χ_2$ - determine the relic abundance analytically. From observations of dwarf and low surface brightness galaxy rotation curves, as well as strong cluster lensing, we place constraints on the microphysics parameters. From these constrained regions, we map the microphysics to effective \texttt{ETHOS} parameters and evolve the linear power spectrum in \texttt{CLASS}. We then confront the model with direct-detection constraints and place an upper bound on our parameter space. We identify a region where: (1) the SIDM dominant component attains $σ_{\rm{eff}}/m = 20 - 40~\text{cm}^{2}\text{g}^{-1}$ at dwarf velocities while satisfying cluster upper bounds $σ_{\rm{eff}}/m < 0.13~\rm{cm}^{2}\rm{g}^{-1}$; (2) a subpercent uSIDM fraction drives accelerated gravothermal collapse in early halos, providing seeds relevant to high-redshift quasar formation and ``little red dots''; and (3) the small-scale cutoff in the matter power spectrum remains consistent with Lyman-$α$ and satellite counts, but exhibits non-standard features, potentially discernible with future observations. The allowed space can be organized by the mediator-to-DM mass ratio and the late-time uSIDM fraction, with a narrow window singled out by the combined cosmological and astrophysical requirements.

Figures (7)

• Figure 1: uSIDM $2\to 2$ processes: number conserving (left), number changing (center), $\overline{\chi}_1\chi_1/\overline{\chi}_2\chi_2\to A'A'$ (right). For the DM to dark photon annihilation, we draw the t-channel; we do not draw the u-channel for simplicity but we do include its contribution to the cross-section. Similarly, for the number conserving $\overline{\chi}_1 \chi_1 \to \overline{\chi}_1 \chi_1$ scattering, we only show the s-channel diagram, but also the t-channel diagram is included in our analysis.
• Figure 2: The conversion and self-annihilation cross-sections of the two dark matter species as a function of the inverse temperature $x$. We use the values $g_{\chi_{1}} = 6.3\times10^{-1}, ~m_{\chi} = 1 ~\rm{GeV}, ~m_{A'} = 2\times10^{-4}~ \rm{GeV}$ to demonstrate the cross-section hierarchy. The conversion cross-section is many orders of magnitude smaller than the annihilation cross-sections and we are thus justified in dropping the corresponding term of the Boltzmann equations. We also plot the non-relativistic expansion (dashed lines) of the annihilation cross-sections to show that indeed at higher values of $x$, both forms agree well.
• Figure 3: The $m_{A'}$ - $m_{\chi}$ parameter plane for fixed coupling constants $g_{\chi_{1}}$ and $g_{\chi_{2}}$. The filled level contours show the dark matter relic abundance $\Omega_{\text{DM}}\text{h}^{2}$. Above the orange line, the $\chi_2$ is in the Born region, and above the blue line $\chi_1$ is in the Born region. The green line corresponds to $\rm \log_{10}\left(\Omega_{\text{DM}}\text{h}^{2}/\Omega_{\text{CDM}}\text{h}^{2}\right) = 0$, i.e., the model yields the correct observed dark matter relic density. The black line shows the threshold for the $\chi\overline{\chi} \to A^\prime A^\prime$ annihilation to occur, and because of thermal energy, for smaller $m_{\chi}$ the production can occur above threshold.
• Figure 4: Left Panel: The favored SIDM parameter space for considerations of the relic density constraint Eq. \ref{['eq:uSIDM_relic_density']} (orange contour) and fixed $m_{\chi}$ values, specified by the corresponding colors shown in the legend. The gray line corresponds to the transition between the quantum region and the Born region, i.e., below the gray line - the weakly-coupled Born approximation is valid, whereas above one must solve the Schrodinger equation for the Yukawa potential via partial wave analysis Tulin:2013teo. The contours correspond to the satisfying dwarf/low-surface brightness galaxy rotation curve $\sigma_{\text{eff}}/m=20\textup{--}40~{\text{cm}^{2}\text{g}^{-1}}$ at $V_{\rm{max}} = (75\pm 25)~\text{km}~\text{s}^{-1}$Roberts_rotation_curve, and strong clustering lensing upper bounds, represented by $\sigma_{\text{eff}}/m < 0.13~\text{cm}^{2}\text{g}^{-1}$ at $V_{\rm{max}}=(1000\pm 55)~\text{km}~\text{s}^{-1}$Andrade:2020lqq. Right panel: The effective cross-section as a function of $V_{\rm{max}}$ for the representative points in the figure legend that correspond to the black crosses in the left panel.
• Figure 5: Using the chosen parameters from Table \ref{['tab:power-spectrum-parameters']}, we plot the corresponding matter power spectrum (top) and transfer function (bottom). The data are from Planck 2018 Planck:2018nkjChabanier:2019eai, DES Y1 DES_Y1, SDSS DR7 SDSS_DR7, eBOSS DR14 Abolfathi_2018, MW Satellite Forecast MW_forecast, and the HERA and EDGES 21-cm projections HERAEDGESMunoz:2019hjh.