Table 2:
Orbital parameters for PSR B1913+16 in the DD framework,
taken from [144].
For PSR B1913+16, three PK parameters are well measured:
the combined gravitational redshift and time dilation parameter
, the advance of periastron
, and the derivative of the orbital period,
. The orbital parameters for this pulsar, measured in the
theory-independent ``DD'' system, are listed in Table
2
[133
,
144
].
The task is now to judge the agreement of these parameters
with GR. A second useful timing formalism is ``DDGR'' [33,
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% [133
]. 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.
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
-
curves for each parameter and to verify that they intersect at a
common point. Figure
7
displays the
and
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
-
plane, do pass the PSR B1913+16 test and possibly
weak-field tests as well [38
]. 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
is
contaminated by several external contributions. Damour and
Taylor [42] consider the full range of possible contributions to
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''
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
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.
![]() |
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 |