The original system: PSR B1913+16

4.2 The original system: PSR B1913+16

The prototypical double-neutron-star binary, PSR B1913+16, was discovered at the Arecibo Observatory [6

] in 1974 [65 ]. 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 [64 , 130 ]. 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.

Table 2: Orbital parameters for PSR B1913+16 in the DD framework, taken from [144

Parameter	Value
Orbital period $Pb$ (d)	0	.	322997462727(5)
Projected semi-major axis $x$ (s)	2	.	341774(1)
Eccentricity $e$	0	.	6171338(4)
Longitude of periastron $ω$ (deg)	226	.	57518(4)
Epoch of periastron $T0$ (MJD)	46443	.	99588317(3)

Advance of periastron $ω˙$ (deg yr^–1)	4	.	226607(7)
Gravitational redshift $γ$ (ms)	4	.	294(1)
Orbital period derivative $obs (P˙b)$ (10^–12)	–2	.	4211(14)

For PSR B1913+16, three PK parameters are well measured: the combined gravitational redshift and time dilation parameter $γ$ , the advance of periastron $˙ω$ , and the derivative of the orbital period, $P˙b$ . The orbital parameters for this pulsar, measured in the theory-independent “DD” system, are listed in Table 2 [132 , 144 ].

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 [144

], courtesy Joel Weisberg.)

The task is now to judge the agreement of these parameters with GR. A second useful timing formalism is “DDGR” [35 , 45 ], 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% [132 ]. The classic demonstration of this agreement is shown in Figure 6 [144 ], in which the observed accumulated shift of periastron is compared to the predicted amount.

Figure 7: Mass–mass diagram for the PSR B1913+16 system, using the $˙ω$ and $γ$ 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 [144

], 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 $m1 –m2$ curves for each parameter and to verify that they intersect at a common point. Figure 7 displays the $˙ω$ and $γ$ 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 $m1 – m2$ plane, do pass the PSR B1913+16 test and possibly weak-field tests as well [36 ]. 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 [35 ]. The second is that the measured value of the orbital period derivative $˙ Pb$ is contaminated by several external contributions. Damour and Taylor [44 ] consider the full range of possible contributions to $P˙b$ 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” $v2∕r$ 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 $˙ Pb$ 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., [84 , 2 ]) which now limits the precision of the test of GR resulting from this system.