White Dwarf Crystallization 2D: Radial Fractionation & Γ Phase Diagram

This is the 2D companion to the 3D particle-box white dwarf sim: the same carbon-oxygen phase-separation physics, computed independently as a radial (mass-coordinate) cross-section instead of a box of discrete freezing ions. The star's mass is discretized into 120 concentric shells; as the crystallization front sweeps outward from the dense center, each shell's oxygen content is set by numerically integrating the real Rayleigh-fractionation equation shell by shell — the same closed-form relation (X_liquid = X₀(1−f)^(k_D−1)) that describes fractional crystallization, verified here to converge to the analytic solution as the shell count increases. A second panel plots the Coulomb-coupling phase diagram Γ(T) for both ion species directly, showing why oxygen's higher charge (Z=8 vs carbon's Z=6) makes it cross the Γ≈175 crystallization threshold at a higher core temperature.