In a gravitationally bound binary system hosting with a minimum of one emitting pulsar, the time of arrival of emitted radio pulses is observed to change, among other things, owing to orbital motion about the common center of mass. This is initiated by a gravitational tug of an unseen companion, which could be a main sequence star, an astrophysical compact object, for example, a neutron star that does not emit pulses or whose pulses are not detectable, a white dwarf, or a black hole.
This periodic variation of orbital origin could be modeled as a ratio of the projection of the barycentric orbit of the pulsar onto the line of sight to the speed of light. To analyze this, researchers have assumed a coordinate system whose center is at the binary center of mass whose reference z-axis points towards the observer along the line of sight in a way that the reference plane coincides with the plane of the sky.
Dr. Lorenzo Iorio from the Italian Ministry of Education, Universities and Research (M.I.U.R.) – Education, Italy, demonstrated a simple and a straightforward method to compute the effect that a number of post-Keplerian features of motion, both post-Newtonian and Newtonian, have on this key observable. This study is published in peer-reviewed journal, The European Physical Journal C.
The author analytically computed the corresponding net time delays per orbital revolution. The instantaneous shifts were considered in a bid to cope with systems that indicated long orbital periods relating to the time spans normally used for data collection. This strategy was valid in the sense that it would be extended to an array of dynamical effects notwithstanding their physical origin that would encompass modified models of gravity.
For this reason, more realistic sensitivity evaluations while aiming at reinterpreting existing studies and designing new ones would have been performed with respect to a closer correspondence with which is actually measured. The author also considered Shapiro-like time delays reference to the propagation of the electromagnetic waves emitted by the visible pulsar in the entire space-time deformed by axisymmetric departures from spherical symmetry of the deflecting bodies.
Lorenzo Iorio devised an approach to compute the shifts experienced by the orbital component of the time change of a binary pulsar p reference to some perturbing post-Keplerian accelerations. The author applied the method to the still hypothetical scenario covering an emitting neutron star orbiting the supermassive black in Sgr A* whose timing accuracy extended up to 1-10 µs or 100 µs.
By assuming an S2-like orbital configuration and a time span as long as its orbital period, the author found the magnitude of the post-Newtonian Schwarzschild-type gravitoelectric signature reached not less than 103 s. The post-Newtonian Lense-Thirring gravitomagnetic as well as quadrupolar effects were smaller dictated by the orientation of the axis of the black hole’spin.
The author also explicitly computed an analytical formula for the Shapiro-like time delay reference to the propagation of electromagnetic waves in the field of a spinning oblate body and applied to the aforementioned binary system. The Shapiro-like time shifts were generally smaller than the orbital ones that were, contrary to Shapiro-like time shifts, cumulative.
From the results of Lorenzo Iorio study, he remarked that the method could be extended to arbitrary orbital geometries and symmetry axis orientations of the binary’s bodies, notwithstanding the disturbing accelerations. It can be applied to other binary systems as probes, and in principle, manufactured binaries could also be considered.
Lorenzo Iorio. Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the galactic center. The European Physical Journal C (2017) 77:439.
Go To The European Physical Journal C