4.4 Combined binary-pulsar tests

Because of their different orbital parameters and inclinations, the double-neutron-star systems PSR B1913+16 and B1534+12 provide somewhat different constraints on alternative theories of gravity. Taken together with some of the limits on SEP violation discussed above, and with solar-system experiments, they can be used to disallow certain regions of the parameter space of these alternate theories. This approach was pioneered by Taylor et al. [133Jump To The Next Citation Point], who combined PK-parameter information from PSRs B1913+16 and B1534+12 and the Damour and Schäfer result on SEP violation by PSR B1855+09 [43Jump To The Next Citation Point] to set limits on the parameters β ′ and β ′′ of a class of tensor-biscalar theories discussed in [36] (Figure 9View Image). In this class of theories, gravity is mediated by two scalar fields as well as the standard tensor, but the theories can satisfy the weak-field solar-system tests. Strong-field deviations from GR would be expected for non-zero values of β′ and β′′, but the theories approach the limit of GR as the parameters β′ and β ′′ approach zero.
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Figure 9: Portions of the tensor-biscalar ′ ′′ β –β plane permitted by timing observations of PSRs B1913+16, B1534+12, and B1855+09 up to 1992. Values lying above the curve labeled “a” are incompatible with the measured ω˙ and γ parameters for PSR B1913+16. The curves labeled “b” and “d” give the allowed ranges of ′ β and ′′ β for PSRs B1913+16 and B1534+12, respectively, fitting for the two neutron-star masses as well as ′ β and ′′ β, using data available up to 1992. The vertical lines labeled “c” represent limits on β′ from the SEP-violation test using PSR B1855+09 [43]. The dot at (0,0) corresponds to GR. (Reprinted by permission from Nature [133],  1992, Macmillan Publishers Ltd.)

A different class of theories, allowing a non-linear coupling between matter and a scalar field, was later studied by Damour and Esposito-Farèse [3840Jump To The Next Citation Point]. The function coupling the scalar field ϕ to matter is given by A (ϕ) = exp(12β0 ϕ2), and the theories are described by the parameters β0 and α0 = β0ϕ0, where ϕ0 is the value that ϕ approaches at spatial infinity (cf. Section 3.3). These theories allow significant strong-field effects when β0 is negative, even if the weak-field limit is small. They are best tested by combining results from PSRs B1913+16, B1534+12 (which contributes little to this test), B0655+64 (limits on dipolar gravitational radiation), and solar-system experiments (Lunar laser ranging, Shapiro delay measured by Viking [114], and the perihelion advance of Mercury [116]). The allowed parameter space from the combined tests is shown graphically in Figure 10View Image [40Jump To The Next Citation Point]. Currently, for most neutron-star equations of state, the solar-system tests set a limit on α0 (2 −3 α 0 < 10) that is a few times more stringent than those set by PSRs B1913+16 and B0655+64, although the pulsar observations do eliminate large negative values of β0. With the limits from the pulsar observations improving only very slowly with time, it appears that solar-system tests will continue to set the strongest limits on α 0 in this class of theories, unless a pulsar–black-hole system is discovered. If such a system were found with a ∼ 10 M ⊙ black hole and an orbital period similar to that of PSR B1913+16 (∼ 8 hours), the limit on α0 derived from this system would be about 50 times tighter than that set by current solar-system tests, and 10 times better than is likely to be achieved by the Gravity Probe B experiment [40Jump To The Next Citation Point].

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Figure 10: The parameter space in the non-linear α0, β0 gravitational theory, for neutron stars described by a polytrope equation of state. The regions below the various curves are allowed by various pulsar timing limits, by solar-system tests (“1PN”), and by projected LIGO/VIRGO observations of NS–NS and NS–BH inspiral events. The shaded region is allowed by all tests. The plane and limits are symmetric about α0 = 0. (From [40]; used by permission.)

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