 Binary-pulsar periastron advance

Binary-pulsar periastron advance is the gradual rotation of the orbit's argument of periapsis $\omega$. A closed Kepler orbit has a fixed direction of closest approach. In general relativity, the leading conservative correction makes the relative orbit precess even before gravitational radiation causes appreciable binary-pulsar orbital decay.

For nonspinning point masses $m_1,m_2$, total mass $M=m_1+m_2$, semimajor axis $a$ of the relative orbit and orbital eccentricity $0<e<1$, the first post-Newtonian advance per orbit isDivide by the orbital period $P_b$ and use Kepler's third law $n^2{a}^3=GM$, where $n=2\pi /P_b$, to obtainHere $\dot{\omega }$ is in radians per unit time. The expansion assumes $GM/[a{c}^2(1-e^2)]\ll 1$.

A pulsar acts as an orbital clock: the timing delay changes as the eccentric orbit turns relative to the line of sight. If this measured advance is dominated by the relativistic point-mass term, then $P_b,e,\dot{\omega }$ determine the total mass $M$, independently of the unknown orbital inclination. They do not separately determine both component masses. A second effect, such as the binary-pulsar Einstein delay, supplies another mass relation; additional timing parameters can then test the theory instead of merely fitting it.^[ref]

Spin-induced quadrupoles, tidal deformation and higher relativistic orders can contribute in other regimes and must be modeled before interpreting all observed precession as this term. At $e=0$, a separate periastron direction is undefined. Advance of this direction is conceptually distinct from decreasing $P_b$: conservative precession by itself is not evidence of radiated orbital energy.