Abstract
Pulsars are fantastic laboratories for studying Gravity in the strong regime (\(GM/r c^2 > .01\)). Pulsars that are part of a binary star system offer even more potential for verifying the predictions of general relativity and comparing it with alternative theories of gravitation. After a quick recap of the astrophysical models for a pulsar, we provide an overview of the techniques that are implemented to record the arrival times of the radio pulses, including the corrections due to position and motion of the Earth and of the pulsar, to interstellar dispersion and to relativistic delays. We then introduce the Post Keplerian (PK) parameters, which allow us to describe purely relativistic phenomena like precessions. As a case study, we apply the relativistic analysis of the orbital motion to two famous binary systems: the so-called Hulse-Taylor pulsar, PSR 1913+16 and the double pulsar PSR J0737+3039: the PK parameters derived for these binaries are again in full agreement with general relativity. Timing analysis of other pulsars contributes to very tight limits on other PPN parameters. Finally, we discuss how the Pulsar Timing Array can provide an effective tool to search for gravitational waves in the nHz band. A worldwide collaboration, coordinating three regional efforts, is pursuing this effort.
The original version of this chapter was revised: Chapter have been updated with the correction. The correction to this chapter can be found at https://doi.org/10.1007/978-3-030-95596-0_15
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Change history
11 April 2023
In original version of the book, the following belated corrections received from the author have been incorporated in respective chapters and Appendix at backmatter.
Chapter 2
Equation 2.27 has been removed and remaining equations are renumbered
Figure 2.8 has been replaced with revised figure
Chapter 7
In Equation 7.20 “(TT)” has been removed from equation
In page 161 the in line equation modified (\( 10^{11} - 10^{15}\) T) to (\( 10^{7} - 10^{11}\) T)
Chapter 9
In Page 215, few lines has been replaced with updated as in below:
From
“In the DL case this difference may be due to different values of the curvature radii of the mirrors of the two cavities while in the FP interferometer, different values of finesse in the two FP cavities, or due to differences in either the radius of curvature or the reflectivity of the mirrors, so one can place even more demanding conditions on the reduction of frequency noise of laser light.”
To
“This difference is due, in both cases, to asymmetries in the practical implementation of the two arms: unequal curvature radii for the DL, unequal finesse (that depends on both the curvature radius and the reflectivity of the mirrors) in the case of the FP cavities. This asymmetry places even more demanding conditions on the reduction of frequency noise of laser light.” In page 218 line has been removed “Although an entire chapter of this text is devoted to it”
In addition, some minor corrections have been made throughout the book that does not change the basic facts.
The correction chapters and the book has been updated with the changes.
Notes
- 1.
The Langmuir waves are rapid oscillations of electron density in the plasma, whose frequency depends only weakly on the wavelength of the oscillation. The plasmon is the quasi-particle resulting from the quantization of these oscillations.
- 2.
In the odd units adopted by pulsar scientists, d is expressed in pc and \(n_e\) in cm\(^{-3}\).
- 3.
Another odd unit of astronomers: measuring star dimensions in terms of the solar radius, \( R_\odot = 6.957 \cdot 10^8~m = 1/215 AU\), as defined in 2015 by the IAU. It is indeed suggestive to think of a two-star system rotating in an orbit that contains just 3 Suns.
- 4.
The Modified Julian Date (MJD) counts the number of days since midnight on November 17, 1858; MJD 52984 is December 11, 2003.
- 5.
An ever-updated catalogue can be found at: https://www.atnf.csiro.au/research/pulsar/psrcat/.
- 6.
In previous sections we used f, but the spin vector is always associated to \(\Omega _p = 2 \pi f \).
- 7.
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Ricci, F., Bassan, M. (2022). Pulsar as Gravitational Laboratory. In: Experimental Gravitation. Lecture Notes in Physics, vol 998. Springer, Cham. https://doi.org/10.1007/978-3-030-95596-0_12
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