Schematic of the unfolding process. The one-dimensional equation set is first solved for the mass density ρ and eccentricity ε along the equatorial axis in the full interval [0, R_e]. Then, the two-dimensional structure is reconstructed by propagating, for each radius (a, 0), the solution (enthalpy, mass density, or pressure) along the ellipse E(a, b) up to the polar axis at (0, b) (see Sect. 2.2).