2001A&A...376..165L

Density fluctuations in convective stars produce small variations of their outer gravitational field that give rise to a very small, though finite, orbital eccentricity in close binaries with convective components. We revisit the theory for such an effect, originally presented by Phinney (1992, Phil. Trans. R. Soc. Lond. A, 341, 39), and propose a new approach to compute the fluctuations of the outer gravitational field based on Chandrasekhar's virial theorem. It is applied to compute the eccentricities of binaries with a millisecond pulsar component in the framework of a simplified model of their evolution. The comparison with the observations allows us to test the models proposed for the formation of such systems, giving support to the evolutionary scenarios that connect them with low-mass X-ray binaries, and to provide a new test for turbulent convection models of giant stars.