Eardley [177] followed the first route and discussed the effects of a time variation of the gravitational
constant on binary pulsar in the framework of the Brans–Dicke theory. In that case, both a dipole
gravitational radiation and the variation of
induce a periodic variation in the pulse period.
Nordtvedt [386
] showed that the orbital period changes as
Damour et al. [127] used the timing data of the binary pulsar PSR 1913+16. They implemented the
effect of the time variation of by considering the effect on
. They defined, in a phenomenological
way, that
, where
is the part of the orbital period derivative that is not
explained otherwise (by gravitational waves radiation damping). This theory-independent definition
has to be contrasted with the theory-dependent result (138
) by Nordtvedt [386]. They got
All the previous results concern binary pulsars but isolated ones can also be used. Heintzmann and
Hillebrandt [248] related the spin-down of the pulsar JP1953 to a time variation of
. The spin-down is a
combined effect of electromagnetic losses, emission of gravitational waves, possible spin-up due to matter
accretion. Assuming that the angular momentum is conserved so that
= constant, one deduces that
Recently, it was argued [266, 432] that a variation of would induce a departure of the neutron star
matter from
-equilibrium, due to the changing hydrostatic equilibrium. This would force non-equilibrium
-processes to occur, which release energy that is invested partly in neutrino emission and partly in
heating the stellar interior. Eventually, the star arrives at a stationary state in which the temperature
remains nearly constant, as the forcing through the change of
is balanced by the ongoing reactions.
Comparing the surface temperature of the nearest millisecond pulsar, PSR J0437-4715, inferred from
ultraviolet observations, two upper limits for variation were obtained,
, direct
Urca reactions operating in the neutron star core are allowed, and
, considering
only modified Urca reactions. This was extended in [302] in order to take into account the
correlation between the surface temperatures and the radii of some old neutron stars to get
.
http://www.livingreviews.org/lrr-2011-2 |
Living Rev. Relativity 14, (2011), 2
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