Relativistic effect of gravitational deflection of light in binary pulsars

Abstract

An improved formula for the timing of binary pulsars that accounts for the relativistic deflection of light in the gravitational field of the pulsar's companion is presented, and the measurability of this effect together with its variance estimates are discussed. The deflection of the pulsar's beam trajectory in the gravitational field of its companion leads to variation in the pulsar's rotational phase. This variation appears as the narrow sharp growth of the magnitude of the post-fit pulsar timing residuals in the vicinity of the moment of the superior conjunction of the pulsar with its companion. In contrast to the relativistic Shapiro effect the amplitude of the effect of gravitational deflection of the pulsar radio beam has two peaks with opposite signs, which become sharper as the inclination $i$ of the pulsar's orbit approaches 90$^{\circ}$. The effect under consideration influences the estimation of parameters of the relativistic Shapiro effect in the binary pulsars with nearly edgewise orbits. Its inclusion in the fitting procedure provide more careful measurement of sine of the orbital inclination $i$ as well as the masses of the pulsar $m_p$ and its companion $m_c$. This permits an improved testing of alternative theories of gravity in the strong field regime. Moreover, the measurement of this effect permits independent geometric constraints on the position of the pulsar rotational axis in space. The effect of the gravitational deflection of light has been numerically investigated for binary pulsars with nearly edgewise orbits. It is shown that the effect is observed in general only when $\cos i\leq 0.003.$ This estimate becomes less restrictive as the pulsar's spin axis approaches the line of the sight.