Testing Theories of Gravitation Using 21-Year Timing of Pulsar Binary J1713+0747

We report 21-yr timing of one of the most precise pulsars: PSR J1713+0747. Its pulse times of arrival are well modeled by a comprehensive pulsar binary model including its three-dimensional orbit and a noise model that incorporates correlated noise such as jitter and red noise. Its timing residuals have weighted root mean square $\sim 92$ ns. The new dataset allows us to update and improve previous measurements of the system properties, including the masses of the neutron star ($1.31\pm0.11$ $M_{\odot}$) and the companion white dwarf ($0.286\pm0.012$ $M_{\odot}$) and the parallax distance $1.15\pm0.03$ kpc. We measured the intrinsic change in orbital period, $\dot{P}^{\rm Int}_{\rm b}$, is $-0.20\pm0.17$ ps s$^{-1}$, which is not distinguishable from zero. This result, combined with the measured $\dot{P}^{\rm Int}_{\rm b}$ of other pulsars, can place a generic limit on potential changes in the gravitational constant $G$. We found that $\dot{G}/G$ is consistent with zero [$(-0.6\pm1.1)\times10^{-12}$ yr$^{-1}$, 95\% confidence] and changes at least a factor of $31$ (99.7\% confidence) more slowly than the average expansion rate of the Universe. This is the best $\dot{G}/G$ limit from pulsar binary systems. The $\dot{P}^{\rm Int}_{\rm b}$ of pulsar binaries can also place limits on the putative coupling constant for dipole gravitational radiation $\kappa_D=(-0.9\pm3.3)\times10^{-4}$ (95\% confidence). Finally, the nearly circular orbit of this pulsar binary allows us to constrain statistically the strong-field post-Newtonian parameters $\Delta$, which describes the violation of strong equivalence principle, and $\hat{\alpha}_3$, which describes a breaking of both Lorentz invariance in gravitation and conservation of momentum. We found, at 95\% confidence, $\Delta<0.01$ and $\hat{\alpha}_3<2\times10^{-20}$ based on PSR J1713+0747.