Igniting Galaxy Formation in the Postreionization Universe, II: Nature versus Nurture

Although the ultraviolet background from reionization is thought to conspire against the smallest halos, some gas-rich halos in the post-reionization Universe still form stars. We ask which properties, environmental or intrinsic, determine ignition. Using the FIREbox cosmological volume, we compare recently-ignited halos to a mass- and gas-matched sample of gas-resolved starless halos at z=2 --6. We test three families of "third axis" properties beyond M vir, M gas, and z: geometric environment (the Perturbation Index and local galaxy density ρ 5), hydrodynamic environment (the 1 -- 2,R vir gas-supply shell), and intrinsic halo properties (concentration and the neutral-gas reservoir). A nested random-forest classification finds that geometric environment adds little, while the hydrodynamic shell is modestly informative. Three complementary properties each discriminate ignited from starless halos beyond the mass--gas--redshift baseline (AUC =0.635, where 0.5 is chance): total HI mass (M HI, AUC =0.739), the extent of the neutral gas (r HI,50/R vir, AUC =0.738), and the central HI density (ρ HI,0, AUC =0.700); jointly they reach AUC =0.823, the highest of any combination we test. At fixed halo mass, gas mass and redshift, recently-ignited halos harbor more HI over a larger radius than their matched controls, and these two enhancements are uncorrelated. The same reservoir sets when ignition can happen: from z=6 to z=0 the median starless halo keeps its gas (+0.05 dex) while its neutral fraction falls by 3.9 dex, so the reservoir is ionized rather than exhausted and the ignition window closes below z 2. In sum, a halo's own neutral-gas reservoir discriminates ignited from starless halos more sharply than its location in the cosmic web -- nature over nurture.