4.3 PSR B1534+12 and other binary 4 Tests of GR - 4.1 Post-Keplerian timing parameters

4.2 The original system: PSR B1913+16 

The prototypical double-neutron-star binary, PSR B1913+16, was discovered at the Arecibo Observatory [96Jump To The Next Citation Point In The Article] in 1974 [62]. Over nearly 30 years of timing, its system parameters have shown a remarkable agreement with the predictions of GR, and in 1993 Hulse and Taylor received the Nobel Prize in Physics for its discovery [61, 131]. In the highly eccentric 7.75-hour orbit, the two neutron stars are separated by only 3.3 light-seconds and have velocities up to 400 km/s. This provides an ideal laboratory for investigating strong-field gravity.

   table888
Table 2: Orbital parameters for PSR B1913+16 in the DD framework, taken from [144Jump To The Next Citation Point In The Article].

For PSR B1913+16, three PK parameters are well measured: the combined gravitational redshift and time dilation parameter tex2html_wrap_inline2625, the advance of periastron tex2html_wrap_inline2773, and the derivative of the orbital period, tex2html_wrap_inline2771 . The orbital parameters for this pulsar, measured in the theory-independent ``DD'' system, are listed in Table  2  [133Jump To The Next Citation Point In The Article, 144Jump To The Next Citation Point In The Article].

  

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Figure 6: The parabola indicates the predicted accumulated shift in the time of periastron for PSR B1913+16, caused by the decay of the orbit. The measured values of the epoch of periastron are indicated by the data points. (From [144Jump To The Next Citation Point In The Article], courtesy Joel Weisberg.)

The task is now to judge the agreement of these parameters with GR. A second useful timing formalism is ``DDGR'' [33Jump To The Next Citation Point In The Article, 43], which assumes GR to be the true theory of gravity and fits for the total and companion masses in the system, using these quantities to calculate ``theoretical'' values of the PK parameters. Thus, one can make a direct comparison between the measured DD PK parameters and the values predicted by DDGR using the same data set; the parameters for PSR B1913+16 agree with their predicted values to better than 0.5% [133Jump To The Next Citation Point In The Article]. The classic demonstration of this agreement is shown in Figure  6  [144Jump To The Next Citation Point In The Article], in which the observed accumulated shift of periastron is compared to the predicted amount.

  

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Figure 7: Mass-mass diagram for the PSR B1913+16 system, using the tex2html_wrap_inline2773 and tex2html_wrap_inline2625 parameters listed in Table  2 . The uncertainties are smaller than the widths of the lines. The lines intersect at the point given by the masses derived under the DDGR formalism. (From [144Jump To The Next Citation Point In The Article], courtesy Joel Weisberg.)

In order to check the self-consistency of the overdetermined set of equations relating the PK parameters to the neutron star masses, it is helpful to plot the allowed tex2html_wrap_inline3199 - tex2html_wrap_inline3401 curves for each parameter and to verify that they intersect at a common point. Figure  7 displays the tex2html_wrap_inline2773 and tex2html_wrap_inline2625 curves for PSR B1913+16; it is clear that the curves do intersect, at the point derived from the DDGR mass predictions.

Clearly, any theory of gravity that does not pass such a self-consistency test can be ruled out. However, it is possible to construct alternate theories of gravity that, while producing very different curves in the tex2html_wrap_inline3199 - tex2html_wrap_inline3401 plane, do pass the PSR B1913+16 test and possibly weak-field tests as well [38Jump To The Next Citation Point In The Article]. Such theories are best dealt with by combining data from multiple pulsars as well as solar-system experiments (see Section  4.4).

A couple of practical points are worth mentioning. The first is that the unknown radial velocity of the binary system relative to the SSB will necessarily induce a Doppler shift in the orbital and neutron-star spin periods. This will change the observed stellar masses by a small fraction but will cancel out of the calculations of the PK parameters [33]. The second is that the measured value of the orbital period derivative tex2html_wrap_inline2771 is contaminated by several external contributions. Damour and Taylor [42] consider the full range of possible contributions to tex2html_wrap_inline2771 and calculate values for the two most important: the acceleration of the pulsar binary centre-of-mass relative to the SSB in the Galactic potential, and the ``Shklovskii'' tex2html_wrap_inline3415 effect due to the transverse proper motion of the pulsar (cf. Section  3.2.2). Both of these contributions have been subtracted from the measured value of tex2html_wrap_inline2771 before it is compared with the GR prediction. It is our current imperfect knowledge of the Galactic potential and the resulting models of Galactic acceleration (see, e.g., [83, 1]) which now limits the precision of the test of GR resulting from this system.



4.3 PSR B1534+12 and other binary 4 Tests of GR - 4.1 Post-Keplerian timing parameters

image Testing General Relativity with Pulsar Timing
Ingrid H. Stairs
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