Astrometric Limits on the Stochastic Gravitational Wave Background

The canonical methods for gravitational wave detection are ground- and space-based laser interferometry, pulsar timing, and polarization of the cosmic microwave background. But as has been suggested by numerous investigators, astrometry offers an additional path to gravitational wave detection. Gravitational waves deflect light rays of extragalactic objects, creating apparent proper motions in a quadrupolar (and higher order modes) pattern. Astrometry of extragalactic radio sources is sensitive to gravitational waves with frequencies between roughly $10^{-18}$ and $10^{-8}$ Hz ($H_0$ and 1/3 yr$^{-1}$), overlapping and bridging the pulsar timing and CMB polarization regimes. We present methodology for astrometric gravitational wave detection in the presence of large intrinsic uncorrelated proper motions (i.e., radio jets). We obtain 95% confidence limits on the stochastic gravitational wave background using 711 radio sources, $\Omega_{GW} < 0.0064$, and using 508 radio sources combined with the first Gaia data release: $\Omega_{GW} < 0.011$. These limits probe gravitational wave frequencies $6\times10^{-18}$ Hz $\lesssim f \lesssim 1\times10^{-9}$ Hz. Using a WISE-Gaia catalog of 567,721 AGN, we predict a limit expected from Gaia alone of $\Omega_{GW} < 0.0006$, which is significantly higher than originally forecast. We incidentally detect and report on 22 new examples of optical superluminal motion with redshifts 0.13-3.89.