Evolutionary Self-Energy-Loss Effects in Compact Binary Systems: Importance of Rapid Rotation and of Equation of State

Abstract

The 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 in long-term high-precision timing measurements of the binary's orbital motion. We use rotating compressible spheroids to obtain an approximate, explicit expression for the orbital period derivative, due to spin-down, valid to 1PN order. This expression can be used to observationally constrain the pulsar's moment of inertia, and, combined with other observations, the high-density equation of state of compact stars. We apply our expression to representative models of millisecond pulsars in binary systems and demonstrate the importance of including higher-order rotational effects as well as the importance of the choice of equation of state, which both have been neglected, so far, in the literature. The computed increase in orbital period is larger, by as much as 32%, when the higher-order rotational effects are included, while it can change by more than a factor of two between different plausible equations of state.