Why I-Love-Q: Explaining why universality emerges in compact objects
similar to each other to explain the universality observed. Second, we study the impact on the universality of approximating stellar isodensity contours as self-similar ellipsoids. An analytical calculation in the non-relativistic limit reveals that the shape of the ellipsoids per se does not aect the universal relations much, but relaxing the selfsimilarity assumption can completely destroy it. Third, we investigate the eccentricity proles of rotating relativistic stars and nd that the ellipticity is roughly constant, with variations of roughly (20{30)% in the region that matters to the universal relations. Fourth, we repeat the above analysis for dierentially-rot ating, non-compact, regular stars and nd that this time the ellipticity is not constant, with variations that easily exceed 100%, and moreover, universality is lost. These ndings suggest that universality arises as an emergent approximate symmetry: as one ows in the stellarstructure phase space from non-compact star region to the relativistic star region, the eccentricity variation inside stars decreases, leading to approximate self-similarity in their isodensity contours, which then leads to the universal behavior observed in their exterior multipole moments.