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Using stellar structure calculations in the Hartle-Thorne approximation, wederive analytic expressions connecting the ellipticity of the stellar surfaceto the compactness, the spin angular momentum, and the quadrupole moment of thespacetime. We also obtain empirical relations between the compactness, the spinangular momentum, and the spacetime quadrupole. Our formulae reproduce theresults of numerical calculations to within a few percent and help reduce thenumber of parameters necessary to model the observational appearance ofmoderately spinning neutron stars. This is sufficient for comparing theoreticalspectroscopic and timing models to observations that aim to measure the massesand radii of neutron stars and to determine the equation of state prevailing intheir interiors.

Relations Between Neutron-Star Parameters in the Hartle-Thorne Approximation