Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the galactic center
Abstract We develop a general approach to analytically calculate the perturbations $$\Delta \delta \tau _\text {p}$$ Δ δ τ p of the orbital component of the change $$\delta \tau _\text {p}$$ δ τ p of the times of arrival of the pulses emitted by a binary pulsar p induced by the post-Keplerian accele...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2017-07-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-017-5008-1 |
| Summary: | Abstract We develop a general approach to analytically calculate the perturbations $$\Delta \delta \tau _\text {p}$$ Δ δ τ p of the orbital component of the change $$\delta \tau _\text {p}$$ δ τ p of the times of arrival of the pulses emitted by a binary pulsar p induced by the post-Keplerian accelerations due to the mass quadrupole $$Q_2$$ Q 2 , and the post-Newtonian gravitoelectric (GE) and Lense–Thirring (LT) fields. We apply our results to the so-far still hypothetical scenario involving a pulsar orbiting the supermassive black hole in the galactic center at Sgr A $$^*$$ ∗ . We also evaluate the gravitomagnetic and quadrupolar Shapiro-like propagation delays $$\delta \tau _\text {prop}$$ δ τ prop . By assuming the orbit of the existing main sequence star S2 and a time span as long as its orbital period $$P_\mathrm{b}$$ P b , we obtain $$\left| \Delta \delta \tau _\text {p}^\text {GE}\right| \lesssim 10^3~\text {s},~\left| \Delta \delta \tau _\text {p}^\text {LT}\right| \lesssim 0.6~\text {s},\left| \Delta \delta \tau _\text {p}^{Q_2}\right| \lesssim 0.04~\text {s}$$ Δ δ τ p GE ≲ 10 3 s , Δ δ τ p LT ≲ 0.6 s , Δ δ τ p Q 2 ≲ 0.04 s . Faster $$\left( P_\mathrm{b}= 5~\text {years}\right) $$ P b = 5 years and more eccentric $$\left( e=0.97\right) $$ e = 0.97 orbits would imply net shifts per revolution as large as $$\left| \left\langle \Delta \delta \tau _\text {p}^\text {GE}\right\rangle \right| \lesssim 10~\text {Ms},~\left| \left\langle \Delta \delta \tau _\text {p}^\text {LT}\right\rangle \right| \lesssim 400~\text {s},\left| \left\langle \Delta \delta \tau _\text {p}^{Q_2}\right\rangle \right| \lesssim 10^3~\text {s}$$ Δ δ τ p GE ≲ 10 Ms , Δ δ τ p LT ≲ 400 s , Δ δ τ p Q 2 ≲ 10 3 s , depending on the other orbital parameters and the initial epoch. For the propagation delays, we have $$\left| \delta \tau _\text {prop}^\text {LT}\right| \lesssim 0.02~\text {s},~\left| \delta \tau _\text {prop}^{Q_2}\right| \lesssim 1~\upmu \text {s}$$ δ τ prop LT ≲ 0.02 s , δ τ prop Q 2 ≲ 1 μ s . The results for the mass quadrupole and the Lense–Thirring field depend, among other things, on the spatial orientation of the spin axis of the Black Hole. The expected precision in pulsar timing in Sgr A $$^*$$ ∗ is of the order of $$100~\upmu \text {s}$$ 100 μ s , or, perhaps, even 1–10 $$\upmu \text {s}$$ μ s . Our method is, in principle, neither limited just to some particular orbital configuration nor to the dynamical effects considered in the present study. |
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| ISSN: | 1434-6044 1434-6052 |