where
I
is the moment of inertia of the neutron star, about
, and
N
is the (conserved) total number of baryons in the star. By
assuming that this represents the
only
contribution to the observed
of PSR B0655+64, in a manner reminiscent of the test of
described above, Goldman then derives an upper limit of
, depending on the stiffness of the neutron star equation of
state. Arzoumanian [5
] applies similar reasoning to PSR J2019+2425 [103], which has a characteristic age of 27 Gyr once the
``Shklovskii'' correction is applied [102]. Again, depending on the equation of state, the upper limits
from this pulsar are
[5
]. These values are similar to those obtained by solar-system
experiments such as laser ranging to the Viking Lander on Mars
(see,
e.g., [115,
59]). Several other millisecond pulsars, once ``Shklovskii'' and
Galactic-acceleration corrections are taken into account, have
similarly large characteristic ages (see,
e.g., [28,
137]).
Applying this equation to the limit on the deviation from GR
of the
for PSR 1913+16, they found a value of
. Nordtvedt [106] took into account the effects of
on neutron-star structure, realizing that the total mass and
angular momentum of the binary system would also change. The
corrected expression for
incorporates the compactness parameter
and is
(Note that there is a difference of a factor of -2 in
Nordtvedt's definition of
versus the Damour definition used throughout this article.)
Nordtvedt's corrected limit for PSR B1913+16 is therefore
slightly weaker. A better limit actually comes from the
neutron-star-white-dwarf system PSR B1855+09, with a
measured limit on
of
[73]. Using Equation (29
), this leads to a bound of
, which Arzoumanian [5
] corrects using Equation (30
) and an estimate of NS compactness to
. Prospects for improvement come directly from improvements to
the limit on
. Even though PSR J1012+5307 has a tighter limit on
[84], its shorter orbital period means that the
limit it sets is a factor of 2 weaker than obtained with
PSR B1855+09.
While some cancellation of ``observed'' mass changes might be
expected from the changes in neutron-star binding energy (cf.
Section
3.4.2
above), these will be smaller than the
changes by a factor of order the compactness and can be
neglected. Also, the claimed variations of the fine structure
constant of order
[140] over the redshift range 0.5 <
z
< 3.5 could introduce a maximum derivative of
of about
and hence cannot influence the Chandrasekhar mass at the same
level as the hypothesized changes in
G
.
One of the five systems used by Thorsett has since been shown
to have a white-dwarf companion [138], but as this is one of the youngest systems, this will not
change the results appreciably. The recently discovered
PSR J1811-1736 [89], a double-neutron-star binary, has a characteristic age of only
and, therefore, will also not significantly strengthen the
limit. Ongoing searches for pulsars in globular clusters stand
the best chance of discovering old double-neutron-star binaries
for which the component masses can eventually be measured.
![]() |
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 |