The Analyticity Parameter of Neutron Star Post-Merger Oscillations

For black hole ringdown, the analyticity parameter ρ = γ₁/γ₀ ≈ 3 is universal — independent of mass, spin, and multipole [Paper I]. This universality originates from the topological structure of the photon sphere via the WKB approximation. Neutron star post-merger oscillations lack a photon sphere; their oscillation spectra depend on the nuclear equation of state (EOS). We compute ρ_NS from numerical relativity simulations of binary neutron star mergers across multiple EOS models and show that ρ_NS is EOS-dependent, ranging from [TBD] to [TBD]. This makes ρ_NS a novel EOS discriminant, complementing the tidal deformability Λ and the dominant post-merger frequency f₂.