4.5 Independent geometrical information: PSR J0437-47154 Tests of GR - 4.3 PSR B1534+12 and other binary

4.4 Combined binary-pulsar tests 

Because of their different orbital parameters and inclinations, the double-neutron-star systems PSRs 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.  [134Jump To The Next Citation Point In The Article], 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 [41Jump To The Next Citation Point In The Article] to set limits on the parameters tex2html_wrap_inline2631 and tex2html_wrap_inline2633 of a class of tensor-biscalar theories discussed in [38] (Figure  9). 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 tex2html_wrap_inline2631 and tex2html_wrap_inline2633, but the theories approach the limit of GR as the parameters tex2html_wrap_inline2631 and tex2html_wrap_inline2633 approach zero.

  

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Figure 9: Portions of the tensor-biscalar tex2html_wrap_inline2631 - tex2html_wrap_inline2633 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 tex2html_wrap_inline2773 and tex2html_wrap_inline2625 parameters for PSR B1913+16. The curves labeled ``b'' and ``d'' give the allowed ranges of tex2html_wrap_inline2631 and tex2html_wrap_inline2633 for PSRs B1913+16 and B1534+12, respectively, fitting for the two neutron-star masses as well as tex2html_wrap_inline2631 and tex2html_wrap_inline2633, using data available up to 1992. The vertical lines labeled ``c'' represent limits on tex2html_wrap_inline2631 from the SEP-violation test using PSR B1855+09 [41]. The dot at (0,0) corresponds to GR. (Reprinted by permission from Nature [134], ©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 [35, 37Jump To The Next Citation Point In The Article]. The function coupling the scalar field tex2html_wrap_inline2677 to matter is given by tex2html_wrap_inline3511, and the theories are described by the parameters tex2html_wrap_inline2651 and tex2html_wrap_inline3515, where tex2html_wrap_inline2681 is the value that tex2html_wrap_inline2677 approaches at spatial infinity (cf. Section  3.3). These theories allow significant strong-field effects when tex2html_wrap_inline2651 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 [116], and the perihelion advance of Mercury [118]). The allowed parameter space from the combined tests is shown graphically in Figure  10  [37Jump To The Next Citation Point In The Article]. Currently, for most neutron-star equations of state, the solar-system tests set a limit on tex2html_wrap_inline2649 (tex2html_wrap_inline3525) 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 tex2html_wrap_inline2651 . 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 tex2html_wrap_inline2649 in this class of theories, unless a pulsar-black-hole system is discovered. If such a system were found with a tex2html_wrap_inline3531 - tex2html_wrap_inline3533 black hole and an orbital period similar to that of PSR B1913+16 (tex2html_wrap_inline3535  hours), the limit on tex2html_wrap_inline2649 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 [37Jump To The Next Citation Point In The Article].

  

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Figure 10: The parameter space in the non-linear tex2html_wrap_inline2649, tex2html_wrap_inline2651 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 tex2html_wrap_inline2653 . (From [37]; used by permission.)


4.5 Independent geometrical information: PSR J0437-47154 Tests of GR - 4.3 PSR B1534+12 and other binary

image Testing General Relativity with Pulsar Timing
Ingrid H. Stairs
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