The orthometric parametrization of the Shapiro delay and an improved test of general relativity with binary pulsars

In this paper, we express the relativistic propagational delay of light in the space-time of a binary system (commonly known as the 'Shapiro delay') as a sum of harmonics of the orbital period of the system. We do this first for near-circular orbits as a natural expansion of an existing orbital model for low-eccentricity binary systems. The amplitudes of the third and higher harmonics can be described by two new post-Keplerian (PK) parameters proportional to the amplitudes of the third and fourth harmonics (h(3), h(4)). For high orbital inclinations we use a PK parameter proportional to the ratio of amplitudes of successive harmonics (sigma) instead of h(4). The new PK parameters are much less correlated with each other than r and s, and provide a superior description of the constraints introduced by the Shapiro delay on the orbital inclination and the masses of the components of the binary. A least-squares fit that uses h(3) always converges, unlike in the case of the (r, s) parametrization; its resulting statistical significance is the best indicator of whether the Shapiro delay has been detected. Until now these constraints could only be derived from Bayesian chi(2) maps of the (cos i, m(c)) space. We show that for low orbital inclinations even these maps overestimate the masses of the components and that this can be corrected by mapping the orthogonal (h(3), h(4)) space instead. Finally, we extend the h(3), sigma parametrization to eccentric binaries with high orbital inclinations. For some such binaries we can measure extra PK parameters and test general relativity using the Shapiro delay parameters. In this case we can use the measurement of h(3) as a test of general relativity. We show that this new test is not only more stringent than the r test, but it is even more stringent than the previous s test. Until now this new parametric test could only be derived statistically from an analysis of a probabilistic chi(2) map.