Reionization Topology as a Probe of Self-Interacting Dark Matter

The topology of cosmic reionization, the sizes, shapes, and connectivity of ionized bubbles is a primary observable of next-generation 21\,cm experiments. We show that this topology is sensitive to the microphysics of dark matter. Self-interacting dark matter (SIDM), with cross-sections $\sigma/m\sim 1$--$10\;\mathrm{cm^2/g}$ motivated by small-scale structure anomalies, reduces halo gas binding energies and increases the duty cycle of ionizing-photon escape. At fixed global neutral fraction $\bar{x}_{\rm HI}$, this reshapes the source population from rare, very bright emitters to more numerous, moderate emitters, producing qualitatively different ionization morphology. We decompose the effect into two scale-dependent levers: a $2$--$3\%$ emissivity-weighted bias shift at $k\lesssim 0.1\;h/\mathrm{Mpc}$, and a factor $2$--$4$ shot-noise suppression at $k\sim 0.1$--$1\;h/\mathrm{Mpc}$. A halo-by-halo semi-numerical simulation at $128^3$ resolution confirms a $\sim 60$--$70\%$ increase in the Euler characteristic of the ionization field for $\sigma/m \gtrsim 2\;\mathrm{cm^2/g}$, detected at $3.8\sigma$ across ten independent realizations. A blowout model connecting the binding-energy reduction to the duty cycle through the ISM column density distribution yields a detection threshold at $\sigma/m \sim 1$--$2\;\mathrm{cm^2/g}$. The signal exceeds the CDM baryonic uncertainty band and is robust to the functional form of the emissivity parametrization. The signal persists even if gravitational heating offsets $50$--$75\%$ of the blowout enhancement, and is not diluted by unresolved low-mass sources. Velocity-dependent SIDM produces a qualitatively distinct opposite-sign bias shift. These predictions are testable with SKA1-Low, establishing reionization as a new arena for probing dark matter models complementary to dwarf galaxies and galaxy clusters.