Evolutionary self-energy-loss effects in compact binary systems - Importance of rapid rotation and of equation of state

fThe spin-down of a millisecond pulsar in a compact binary system leads to self-energy losses, that cause the binary's orbital period to increase (the effect being of first post-Newtonian (1PN) order). If the pulsar's period- derivative is not exceedingly small, this effect can become measurable ill long-term high-precision timing measurements of the binary's orbital motion . We use rotating compressible spheroids to obtain all approximate, explici t expression for the orbital period derivative, due to spin-down, valid to IPN order. This expression can be used to observationally constrain the pul sar's moment of inertia, and, combined with other observations. the high-de nsity equation of state of compact stars. We apply our expression to repres entative models of millisecond pulsars in binary systems and demonstrate th e importance of including higher-order rotational effects as well as the im portance of the choice of equation of state, which both have been neglected , so far, in the literature. The computed increase in orbital period is lar ger, by as much as 32%, when the higher-order I rotational effects are incl uded, while it can change by more than a factor of two between different pl ausible equations of state.