Table 3:
Orbital parameters for PSR B1534+12 in the DD framework,
taken from [125].
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
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
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 [132], which together yield a value of
. 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 [17,
121
]. The most recent value of the distance derived in this manner
is
[125
]. (Note that the newer ``NE2001'' Galactic model [30] 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
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., [121,
7,
71]) - 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 [74].
Despite the problematic correction to
, 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
,
, 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 [2,
3] is in the globular cluster M15. While its orbital period
derivative has been measured [44], 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 PSRs J1518+4904 [101] and J1811-1736 [89] have such wide orbits that, although
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
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 [72
], 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
from a mass quadrupole of the companion.
![]() |
Testing General Relativity with Pulsar Timing
Ingrid H. Stairs http://www.livingreviews.org/lrr-2003-5 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |