where
in GR, and
is the coupling strength of body ``
i
'' to a scalar gravitational field [35
]. (Similar expressions can be derived when casting
in terms of the parameters of specific tensor-scalar theories,
such as Brans-Dicke theory [23]. Equation (27
), however, tests a more general class of theories.) Of course,
the best test systems here are pulsar-white-dwarf binaries with
short orbital periods, such as PSR B0655+64 and
PSR J1012+5307, where
so that a strong limit can be set on the coupling of the pulsar
itself. For PSR B0655+64, Damour and Esposito-Farèse [35
] used the observed limit of
[5
] to derive
(1-
, where
is a reference value of the coupling at infinity. More recently,
Arzoumanian [6] has set a somewhat tighter 2-
upper limit of
, or
, which yields
. For PSR J1012+5307, a ``Shklovskii'' correction
(see [119] and Section
3.2.2) for the transverse motion of the system and a correction for
the (small) predicted amount of quadrupolar radiation must first
be subtracted from the observed upper limit to arrive at
and
at 95% confidence [84
]. It should be noted that both these limits depend on estimates
of the masses of the two stars and do not address the (unknown)
equation of state of the neutron stars.
Limits may also be derived from double-neutron-star systems (see, e.g., [148, 151]), although here the difference in the coupling constants is small and so the expected amount of dipolar radiation is also small compared to the quadrupole emission. However, certain alternative gravitational theories in which the quadrupolar radiation predicts a positive orbital period derivative independently of the strength of the dipolar term (see, e.g., [117, 99, 85]) are ruled out by the observed decreasing orbital period in these systems [142].
Other pulsar-white-dwarf systems with short orbital periods
are mostly found in globular clusters, where the cluster
potential will also contribute to the observed
, or in interacting systems, where tidal effects or magnetic
braking may affect the orbital evolution (see,
e.g., [4,
50,
100]). However, one system that offers interesting prospects is the
recently discovered PSR J1141-6545 [72
], which is a young pulsar with white-dwarf companion in a
4.75-hour orbit. In this case, though, the pulsar was formed
after
the white dwarf, instead of being recycled by the white-dwarf
progenitor, and so the orbit is still highly eccentric. This
system is therefore expected both to emit sizable amounts of
quadrupolar radiation -
could be measurable as soon as 2004 [72
] - and to be a good test candidate for dipolar emission [52].
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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 |