Gravitational-wave versus binary-pulsar tests of strong-field gravity

TL;DR

This work addresses testing strong-field gravity by comparing binary pulsar timing and gravitational-wave observations within a two-parameter tensor-scalar framework defined by $A(\varphi)=\exp\left(\frac{1}{2}\beta_0 \varphi^2\right)$. It maps theory parameters to neutron-star properties using realistic equations of state, revealing nonperturbative strong-field effects when $\beta_0$ is negative and below a critical value $\beta_c$. It derives the gravitational-wave phase evolution, showing the dominant scalar-dipole contribution enters as a term proportional to $b\,\nu^{2/5}u^{-2/3}$ with $b=\frac{5}{96}\kappa^{-3/5}(1+\alpha_A\alpha_B)^{-2/5}(\alpha_A-\alpha_B)^2$, and translates Will-like bounds into constraints on $(\alpha_A-\alpha_B)^2$. The main conclusion is that GW tests, for realistic equations of state, are typically less constraining than present binary-pulsar tests for strong-field deviations, though GW observations provide crucial independent tests and could be competitive in favorable NS-BH or nearby NS-NS events; EOS softness enhances pulsar constraints, while finite-size effects are negligible.

Abstract

Binary systems comprising at least one neutron star contain strong gravitational field regions and thereby provide a testing ground for strong-field gravity. Two types of data can be used to test the law of gravity in compact binaries: binary pulsar observations, or forthcoming gravitational-wave observations of inspiralling binaries. We compare the probing power of these two types of observations within a generic two-parameter family of tensor-scalar gravitational theories. Our analysis generalizes previous work (by us) on binary-pulsar tests by using a sample of realistic equations of state for nuclear matter (instead of a polytrope), and goes beyond a previous study (by C.M. Will) of gravitational-wave tests by considering more general tensor-scalar theories than the one-parameter Jordan-Fierz-Brans-Dicke one. Finite-size effects in tensor-scalar gravity are also discussed.

Figures (5)

• Figure 1: Region of the $(\alpha_0,\beta_0)$ theory plane allowed by solar-system tests, binary-pulsar experiments, and future gravity-wave detections, in the case where nuclear matter is described by the polytrope (\ref{['eq2.4']})-(\ref{['eq2.5']}). In view of the reflection symmetry $\alpha_0\rightarrow -\alpha_0$, we plot only the upper half plane. The region allowed by solar-system tests is below the thin line labeled "1PN". The PSR 0655+64 data constrain the values of $\alpha_0$ and $\beta_0$ to be between the two solid lines. The regions allowed by the PSR 1913+16 and PSR 1534+12 tests lie respectively to the right of the bold line and of the the dashed line. The horn-shaped region at the top-left of the dashed line is removed if the observable $\dot P_b^{\rm obs}$ is taken into account for PSR 1534+12. Each of these curves determines the level $\chi^2 = 1$ for the corresponding test. We have also plotted the level $\chi^2 = 2$ for PSR 1913+16 to underline that the precise value of $\chi^2$ is not very significant in the region where binary-pulsar experiments are more constraining than solar-system tests ($\beta_0\,{\lesssim}-3$). The regions excluded by the gravity-wave observation limit (\ref{['eq3.10']}), with a signal-to-noise ratio $S/N = 10$, lie on the hatched sides of the curves labeled "LIGO/VIRGO". The case of a $1.4\,m_\odot$-neutron-star and a $10\,m_\odot$-black-hole binary system is labeled "NS-BH", whereas the case of a 1913+16-like binary-neutron-star system is labeled "NS-NS". The region simultaneously allowed by all the tests is shaded.
• Figure 2: Same plot as Fig. 1 in the case of a soft equation of state (Pandharipande). The region possibly excluded by the LIGO/VIRGO detection of a ($1.4\,m_\odot$) neutron star--($10\,m_\odot$) black hole system lies above the dotted line. The bubble-like region at the left of Fig. 1 (binary-neutron-star system detected by LIGO/VIRGO) does not exist in the case of this soft equation of state.
• Figure 3: Same plot as Fig. 2 for a medium equation of state (Wiringa et al.). Dotted lines indicate the regions excluded by future gravitational-wave observations, respectively inside the bubble for the NS-NS case, and above the straight line for the NS-BH case.
• Figure 4: Same plot as Fig. 3 for a stiff equation of state (Haensel et al.). Note that the bubble excluded by the detection of a binary-neutron-star system by LIGO/VIRGO is much larger when the equation of state is stiff.
• Figure 5: Same plot as Fig. 1, assuming the same polytropic equation of state, but a signal-to-noise ratio $S/N = 100$ for the LIGO (hatched) curves. For clarity, the dashed line corresponding to the PSR 1534+12 test has been suppressed.