The factors 0(q, r0, n) and 0'(q, r0, n) express the fact that a star in a binary system has a volume slightly larger than that of a single star of identical mass. Intuitively this is clear because the gravitational acceleration of a single star is reduced by the presence of the companion and the orbital rotation, and thus the density decreases. This systematic deviation needs to be considered when comparing stellar radii derived from EBs with those predicted by models describing stellar structure. For close systems with r0 « 0.3 this causes deviations in radius up to 1%.

Expansion (3.1.48) shows that up to O(r6) a rotating, tidally deformed polytrope can be approximated by a triaxial ellipsoid if rotation is sufficiently slow and tides are sufficiently small. This result provides the foundation of ellipsoidal models. In the case of synchronous rotation (F = 1) and almost circular orbits, the axes (a, b, c) of the ellipsoid only depend on r0, mass ratio q, and polytropic index n

i1 + 6(1 + 7q )^2^03\ 1 + 6(1 - 2q)^2^03 - 6(2 + 5qM2/0V

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