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6.1 Brans–Dicke gravity and the orbital decay of binary systems with neutron stars

Binary stellar systems that are currently known to harbor at least one neutron star have orbital separations that are too large to be used in probing directly strong gravitational fields. Even at that separation, however, the orbital evolution of the binary system caused by the emission of gravitational waves is affected, in a scalar-tensor theory, by the coupling of matter to the scalar field, which occurs in a strong gravitational field. This manifests itself as a violation of the strong equivalence principle, with many observable consequences such as the rapid decay of the orbit due to emission of dipole radiation [54182Jump To The Next Citation Point]. The various quantitative tests of strong-field gravity using binary systems with radio pulsars have been reviewed in detail elsewhere [157]. Here, I will focus only on tests that involve the orbital period evolution of the binary systems.

The best studied binaries with compact objects are the double neutron stars, with the Hulse–Taylor pulsar (PSR 1913+16) as the prototypical case. Unfortunately, in all double neutron-star systems, the masses of the two members of the binary are surprisingly similar [166] and this severely limits the prospects of placing strong constraints on the dipole radiation from them. Indeed, the magnitude of dipole radiation depends on the difference of the sensitivities between the two members of the binaries, and for neutron stars the sensitivities depend primarily on their masses. The resulting constraint imposed on the Brans–Dicke parameter ω by the Hulse–Taylor pulsar is significantly smaller than the limit ω > 40,000 set by the Cassini mission [15].

The constraint is significantly improved when studying binary systems in which only one of the two stars is a neutron star. There are several known neutron star-white dwarf binaries that are suitable for this purpose, in which the neutron stars appear as radio pulsars (e.g., PSR B0655+64 [40Jump To The Next Citation Point], PSR J0437–4715 [172]), as millisecond accreting X-ray pulsars (e.g., XTE J1808–456 [125Jump To The Next Citation Point]), or as non-pulsing X-ray sources (e.g., 4U 1820–30 [182]). In the last two cases, the evolution of the binary orbit is also affected significantly by mass transfer from the companion star to the neutron star. However, for each value of the Brans–Dicke parameter ωBD, there is a minimum absolute value for the rate of evolution of the orbital period (see Figure 14View Image and [125]). An accurate measurement of the orbital period derivative in any of these systems offers, therefore, the potential of placing a lower limit on the Brans–Dicke parameter. Because of the astrophysical complications introduced by mass transfer, the optimal constraint on ωBD is of order 104 in this method, which is comparable to the Cassini limit.

View Image

Figure 15: Constraints on the two parameters of a second-order scalar-tensor theory placed by the timing properties of binary stellar systems that harbor neutron stars (SEP stands for tests of the strong equivalence principle). The constraints imposed by solar system tests, including the Cassini mission, are also shown for comparison [38]. In all cases, the allowed part of the parameter space is under the corresponding curve.

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