2020ApJ...898...69M

General relativity is a fully conservative theory, but there exist other possible metric theories of gravity. We consider nonconservative ones with a parameterized post-Newtonian parameter, ζ₂. A nonzero ζ₂ induces a self-acceleration for the center of mass of an eccentric binary pulsar system, which contributes to the second time derivative of the pulsar spin frequency, 1. In our work, using Will's method, we provide an improved analysis with four well-timed, carefully chosen binary pulsars. In addition, we extend Will's method and derive the effect of ζ₂ on the third time derivative of the spin frequency, \dddotν. For PSR B1913+16, the constraint from \dddotνis even tighter than that from 1. We combine multiple pulsars with Bayesian inference, and obtain the upper limit, |ζ₂|< 1.3×10^–5 at the 95% confidence level, assuming a flat prior in log₁₀|ζ₂|. It improves the existing bound by a factor of 3. Moreover, we propose an analytical timing formalism for ζ₂. Our simulated times of arrival with simplified assumptions show the capability of binary pulsars in limiting ζ₂, and useful clues are extracted for real-data analysis in future. In particular, we discover that for PSRs B1913+16 and J0737-3039A, \dddotνcan yield more constraining limits than 1.