A new limit on local Lorentz invariance violation of gravity from solitary pulsars

Gravitational preferred frame effects are generally predicted by alternative theories that exhibit an isotropic violation of local Lorentz invariance of gravity. They are described by three parameters in the parametrized post-Newtonian formalism. One of their strong-field generalizations, $\hat \alpha_2$, induces a precession of a pulsar's spin around its movement direction with respect to the preferred frame. We constrain $\hat \alpha_2$ by using the non-detection of such a precession using the characteristics of the pulse profile. In our analysis we use a large number of observations from the 100-m Effelsberg radio telescope, which cover a time span of approximately 15 years. By combining data from two solitary millisecond pulsars, PSRs B1937+21 and J1744-1134, we get a limit of $|\hat \alpha_2| < 1.6 \times 10^{-9}$ at 95% confidence level, which is more than two orders of magnitude better than its best weak-field counterpart from the Solar system.