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

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 $\chi_1\chi_1 \to \chi_2\chi_2$ - 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 $\sigma_{\rm{eff}}/m = 20 - 40~\text{cm}^{2}\text{g}^{-1}$ at dwarf velocities while satisfying cluster upper bounds $\sigma_{\rm{eff}}/m < 0.13~\rm{cm}^{2}\rm{g}^{-1}$; (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-$\alpha$ 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.