Nine relativistic binary neutron star systems with orbital periods less than a day are now known. While
some are less interesting for testing relativity, some have yielded interesting tests, and others, notably the
recently discovered “double pulsar” are likely to produce significant results in the future. Here we describe
some of the more interesting or best studied cases; the parameters of the first four are listed in
Table 7.
B1534+12
This is a binary pulsar system in our galaxy [245, 243, 18]. Its pulses are significantly stronger
and narrower than those of B1913+16, so timing measurements are more precise, reaching
3 s accuracy. The orbital plane appears to be almost edge-on relative to the line of sight
(i 80°); as a result the Shapiro delay is substantial, and separate values of the parameters
r and s have been obtained with interesting accuracy. Assuming GR, one infers that the two
masses are and . The rate of orbit decay
agrees with GR to about 15 percent, but the precision is limited by the poorly known
distance to the pulsar, which introduces a significant uncertainty into the subtraction of galactic
acceleration. Independently of , measurement of the four other post-Keplerian parameters
gives two tests of strong-field gravity in the non-radiative regime [253].
B2127+11C
This system appears to be a clone of the Hulse–Taylor binary pulsar, with very similar values
for orbital period and eccentricity (see Table 7). The inferred total mass of the system is
. But because the system is in the globular cluster M15 (NGC 7078), it
suffers Doppler shifts resulting from local accelerations, either by the mean cluster gravitational
field or by nearby stars, that are more difficult to estimate than was the case with the galactic
system B1913+16. This makes a separate, precision measurement of the relativistic contribution
to essentially impossible.
J0737-3039A, B
This binary pulsar system, discovered in 2003 [48], was already remarkable for its
extraordinarily short orbital period (0.1 days) and large periastron advance (16.88° yr^{–1}),
but then the companion was also discovered to be a pulsar [175]. Because two projected
semi-major axes can now be measured, one can obtain the mass ratio directly from the ratio
of the two values of a_{p} sin i, and thereby obtain the two masses by combining that ratio
with the periastron advance, assuming GR. The results are and
, where A denotes the primary (first) pulsar. From these values,
one finds that the orbit is nearly edge-on, with sin i = 0.9991, a value which is completely
consistent with that inferred from the Shapiro delay parameter (see Table 7). In fact, the five
measured post-Keplerian parameters plus the ratio of the projected semi-major axes give six
constraints on the masses (assuming GR): All six overlap within their measurement errors. This
system provides a unique opportunity for tight tests of strong-field and radiative effects in GR.
Furthermore, it is likely that galactic proper motion effects will play a significantly smaller role
in the interpretation of measurements than they did in B1913+16.
J1141-6545
This is a case where the companion is probably a white dwarf [20, 18]. The masses of
the pulsar and companion are and , respectively. has
been measured to about 25 percent, consistent with the GR prediction. But because of the
asymmetry in sensitivities (, ), there is the possibility, absent in the
double neutron-star systems, to place a strong bound on scalar-tensor gravity (see Section 5.4).
J1756-2251
Discovered in 2004, this pulsar is in a binary system with a probable neutron star companion,
with P_{b} = 7.67 hr, e = 0.18, and = 2.585 0.002 deg yr^{–1}[104].
J1906+0746
The discovery of this system was reported in late 2005 [174]. It is a young, 144-ms pulsar in a
relativistic orbit with P_{b} = 3.98 hr, e = 0.085, and = 7.57 0.03 deg yr^{–1}.
Table 7:
Parameters of other binary pulsars. References may be found in the text; for an online catalogue of pulsars
with reasonably up-to-date parameters, see [18].