PSR B1534+12 and other binary pulsars

4.3 PSR B1534+12 and other binary pulsars

A second double-neutron-star binary, PSR B1534+12, was discovered during a drift-scan survey at Arecibo Observatory in 1990 [153 ]. This system is quite similar to PSR B1913+16: It also has a short (10.1-hour) orbit, though it is slightly wider and less eccentric. PSR B1534+12 does possess some notable advantages relative to its more famous cousin: It is closer to the Earth and therefore brighter; its pulse period is shorter and its profile narrower, permitting better timing precision; and, most importantly, it is inclined nearly edge-on to the line of sight from the Earth, allowing the measurement of Shapiro delay as well as the 3 PK parameters measurable for PSR B1913+16. The orbital parameters for PSR B1534+12 are given in Table 3 [125

Table 3: Orbital parameters for PSR B1534+12 in the DD framework, taken from [125

Parameter	Value
Orbital period $Pb$ (d)	0	.	420737299122(10)
Projected semi-major axis $x$ (s)	3	.	729464(2)
Eccentricity $e$	0	.	2736775(3)
Longitude of periastron $ω$ (deg)	274	.	57679(5)
Epoch of periastron $T0$ (MJD)	50260	.	92493075(4)

Advance of periastron $ω˙$ (deg yr^–1)	1	.	755789(9)
Gravitational redshift $γ$ (ms)	2	.	070(2)
Orbital period derivative $obs (P˙b)$ (10^–12)	$−$ 0	.	137(3)
Shape of Shapiro delay $s$	0	.	975(7)
Range of Shapiro delay $r$ ( $μs$ )	6	.	7(1.0)

As for PSR B1913+16, a graphical version of the internal consistency test is a helpful way to understand the agreement of the measured PK parameters with the predictions of GR. This is presented in Figure 8 . It is obvious that the allowed-mass region derived from the observed value of $P˙b$ does not in fact intersect those from the other PK parameters. This is a consequence of the proximity of the binary to the Earth, which makes the “Shklovskii” contribution to the observed $˙ Pb$ much larger than for PSR B1913+16. The magnitude of this contribution depends directly on the poorly known distance to the pulsar. At present, the best independent measurement of the distance comes from the pulsar’s dispersion measure and a model of the free electron content of the Galaxy [131 ], which together yield a value of 0.7 ± 0.2 kpc. If GR is the correct theory of gravity, then the correction derived from this distance is inadequate, and the true distance can be found by inverting the problem [18 , 120 ]. The most recent value of the distance derived in this manner is 1.02 ± 0.05 kpc [125 ]. (Note that the newer “NE2001” Galactic model [32 ] incorporates the GR-derived distance to this pulsar and hence cannot be used in this case.) It is possible that, in the long term, a timing or interferometric parallax may be found for this pulsar; this would alleviate the $˙ Pb$ discrepancy. The GR-derived distance is in itself interesting, as it has led to revisions of the predicted merger rate of double-neutron-star systems visible to gravitational-wave detectors such as LIGO (see, e.g., [120 , 9 , 72 ]) – although recent calculations of merger rates determine the most likely merger rates for particular population models and hence are less vulnerable to distance uncertainties in any one system [75 ].

Figure 8: Mass–mass diagram for the PSR B1534+12 system. Labeled curves illustrate 68% confidence ranges of the DD parameters listed in Table 3. The filled circle indicates the component masses according to the DDGR solution. The kinematic correction for assumed distance d = 0.7 ± 0.2 kpc has been subtracted from the observed value of $P˙ b$ ; the uncertainty on this kinematic correction dominates the uncertainty of this curve. A slightly larger distance removes the small apparent discrepancy between the observed and predicted values of this parameter. (After [125 ].)

Despite the problematic correction to $˙ Pb$ , the other PK parameters for PSR B1534+12 are in excellent agreement with each other and with the values predicted from the DDGR-derived masses. An important point is that the three parameters $ω˙$ , $γ$ , and $s$ (shape of Shapiro delay) together yield a test of GR to better than 1%, and that this particular test incorporates only “quasi-static” strong-field effects. This provides a valuable complement to the mixed quasi-static and radiative test derived from PSR B1913+16, as it separates the two sectors of the theory.

There are three other confirmed double-neutron-star binaries at the time of writing. PSR B2127+11C [4 , 3 ] is in the globular cluster M15. While its orbital period derivative has been measured [46 ], this parameter is affected by acceleration in the cluster potential, and the system has not yet proved very useful for tests of GR, though long-term observations may demonstrate otherwise. The two binaries PSR J1518+4904 [99 ] and J1811–1736 [90 ] have such wide orbits that, although $ω˙$ is measured in each case, prospects for measuring further PK parameters are dim. In several circular pulsar–white-dwarf binaries, one or two PK parameters have been measured – typically $ω˙$ or the Shapiro delay parameters – but these do not over-constrain the unknown masses. The existing system that provides the most optimistic outlook is again the pulsar–white-dwarf binary PSR J1141–6545 [73 ], for which multiple PK parameters should be measurable within a few years – although one may need to consider the possibility of classical contributions to the measured $ω˙$ from a mass quadrupole of the companion.