Strong Equivalence Principle: Dipolar gravitational radiation

3.3 Strong Equivalence Principle: Dipolar gravitational radiation

General relativity predicts gravitational radiation from the time-varying mass quadrupole of a binary pulsar system. The spectacular confirmation of this prediction will be discussed in Section 4 below. GR does not, however, predict dipolar gravitational radiation, though many theories that violate the SEP do. In these theories, dipolar gravitational radiation results from the difference in gravitational binding energy of the two components of a binary. For this reason, neutron-star–white-dwarf binaries are the ideal laboratories to test the strength of such dipolar emission. The expected rate of change of the period of a circular orbit due to dipolar emission can be written as [149 , 38

]

where $G = G ∗$ in GR, and $α ci$ is the coupling strength of body “i” to a scalar gravitational field [38

]. (Similar expressions can be derived when casting $˙ Pb dipole$ in terms of the parameters of specific tensor-scalar theories, such as Brans–Dicke theory [24 ]. Equation (27

), however, tests a more general class of theories.) Of course, the best test systems here are pulsar–white-dwarf binaries with short orbital periods, such as PSR B0655+64 and PSR J1012+5307, where $αc1 ≫ αc2$ so that a strong limit can be set on the coupling of the pulsar itself. For PSR B0655+64, Damour and Esposito-Farèse [38

] used the observed limit of $˙ −13 Pb = (1 ± 4) × 10$ [7

] to derive $(αc1 − α0)2 < 3 × 10−4$ (1- $σ)$ , where $α0$ is a reference value of the coupling at infinity. More recently, Arzoumanian [8 ] has set a somewhat tighter 2- $σ$ upper limit of $|P˙b∕Pb | < 1 × 10−10 yr−1$ , or $|P˙b| < 2.7 × 10−13$ , which yields $(αc − α0)2 < 2.7 × 10−4 1$ . For PSR J1012+5307, a “Shklovskii” correction (see [117 ] and Section 3.2.2) for the transverse motion of the system and a correction for the (small) predicted amount of quadrupolar radiation must first be subtracted from the observed upper limit to arrive at $P˙b = (− 0.6 ± 1.1) × 10−13$ and $(αc1 − α0)2 < 4 × 10−4$ at 95% confidence [85

]. It should be noted that both these limits depend on estimates of the masses of the two stars and do not address the (unknown) equation of state of the neutron stars.

Limits may also be derived from double-neutron-star systems (see, e.g., [147 , 152 ]), although here the difference in the coupling constants is small and so the expected amount of dipolar radiation is also small compared to the quadrupole emission. However, certain alternative gravitational theories in which the quadrupolar radiation predicts a positive orbital period derivative independently of the strength of the dipolar term (see, e.g., [115 , 97 , 86 ]) are ruled out by the observed decreasing orbital period in these systems [142 ].

Other pulsar–white-dwarf systems with short orbital periods are mostly found in globular clusters, where the cluster potential will also contribute to the observed $˙ Pb$ , or in interacting systems, where tidal effects or magnetic braking may affect the orbital evolution (see, e.g., [5 , 52 , 98 ]). However, one system that offers interesting prospects is the recently discovered PSR J1141–6545 [73 ], which is a young pulsar with white-dwarf companion in a 4.75-hour orbit. In this case, though, the pulsar was formed after the white dwarf, instead of being recycled by the white-dwarf progenitor, and so the orbit is still highly eccentric. This system is therefore expected both to emit sizable amounts of quadrupolar radiation – $P˙b$ could be measurable as soon as 2004 [73 ] – and to be a good test candidate for dipolar emission [54 ].