New tests of local Lorentz invariance of gravity with small-eccentricity binary pulsars

Some alternative gravity theories allow the Universal matter distribution to single out the existence of a preferred frame, which breaks the symmetry of local Lorentz invariance (LLI) for the gravitational interaction. In the post-Newtonian parametrization of semi-conservative gravity theories, LLI violation is characterized by two parameters, α1 and α2. In binary pulsars, the isotropic violation of Lorentz invariance in the gravitational sector should lead to characteristic preferred frame effects (PFEs) in the orbital dynamics, if the barycenter of the binary is moving relative to the preferred frame with a velocity w. For small-eccentricity binaries, the effects induced by α-hat1 and α-hat2 (the hat indicates possible modifications by strong-field effects) decouple, and can therefore be tested independently. We use recent timing results of two compact pulsar-white dwarf binaries with known three-dimensional velocity, PSRs J1012+5307 and J1738+0333 to constrain PFEs for strongly self-gravitating bodies, by assuming the isotropic cosmic microwave background to single out a preferred frame. The time derivative of the projected semi-major axis is used to constrain a precession of the orbital plane around w due to PFEs. From this, we derive a limit |α-hat2| < 1.8 x 10-4 at 95% confidence level, which is the most constraining limit for strongly self-gravitating systems up to now, however, still three orders of magnitude weaker than the best Solar system limit for the corresponding weak-field parameter α2. Concerning α-hat1, we propose a new, robust method to constrain this parameter, which avoids the probabilistic considerations inherent in previous methods. This method is based on the fact that a PFE-induced intrinsic eccentricity cannot stay unobserved during a long-term observation due to the significant precession of periastron in binary pulsar with short orbital periods. Our most conservative result, α-hat1 = -0.4-3.1+3.7 x 10-5 at 95% confidence level from PSR J1738+0333, constitutes a significant improvement compared to current most stringent limits obtained both in the Solar system and binary pulsar tests. We also derive corresponding limits for α-hat1 and α-hat2 for a preferred frame that is at rest with respect to our Galaxy, and preferred frames that locally co-move with the rotation of our Galaxy. These limits will continue to improve significantly with future pulsar timing observations conducted at large radio telescopes. Communicated by C M Will (paper)