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  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 by the Hulse–Taylor pulsar is significantly smaller than the limit set by the Cassini mission .
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 , PSR J0437–4715 ), as millisecond accreting X-ray pulsars (e.g., XTE J1808–456 ), or as non-pulsing X-ray sources (e.g., 4U 1820–30 ). 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 , there is a minimum absolute value for the rate of evolution of the orbital period (see Figure 14 and ). 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 is of order 104 in this method, which is comparable to the Cassini limit.
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