Differential Rotation in Convective Envelopes: Constraints from Eclipsing Binaries

Over time, tides synchronize the rotation periods of stars in a binary system to the orbital period. However, if the star exhibits differential rotation then only a portion of it can rotate at the orbital period, so the rotation period at the surface may not match the orbital period. The difference between the rotation and orbital periods can therefore be used to infer the extent of the differential rotation. We use a simple parameterization of differential rotation in stars with convective envelopes in circular orbits to predict the difference between the surface rotation period and the orbital period. Comparing this parameterization to observed eclipsing binary systems, we find that in the surface convection zones of stars in short-period binaries there is very little radial differential rotation, with $|r\partial_r \ln \Omega| < 0.02$. This holds even for longer orbital periods, though it is harder to say which systems are synchronized at long periods, and larger differential rotation is degenerate with asynchronous rotation.