A New Approach to the Low-frequency Stochastic Gravitational-wave Background: Constraints from Quasars and the Astrometric Hellings-Downs Curve

We present new astrometric constraints on the stochastic gravitational-wave background and construct the first astrometric Hellings-Downs curve using quasar proper motions. From quadrupolar vector spherical harmonic fits to the Gaia proper motions of 1,108,858 quasars, we obtain a frequency-integrated upper limit on the gravitational-wave energy density, h702 Omega GW <= 0.023 (95% confidence limit), for frequencies between 11.2 nHz and 3.1 x 10-9 nHz (1.33/t0). However, from the astrometric Hellings-Downs curve that describes the correlated proper motions between 2,104,609,881 quasar pairs as a function of their angular separation, we find a stronger constraint: a characteristic strain of hc <= 2.7 x 10-12 for fref = 1 yr-1 and h702 Omega GW <= 0.0096 at 95% confidence. We probe down to +/- 0.005 mu as2 yr-2 in correlated power and obtain the lowest astrometric limit to date. This is also the first time that optical wavelength astrometry surpasses limits from radio-frequency interferometry. This astrometric analysis does not yet reach the sensitivity needed to detect the pulsar timing-based red gravitational-wave spectrum extrapolated to the quasar gravitational-wave sensitivity window, assuming that the turnover in the spectrum occurs at similar to 1 nHz for massive black hole binaries. The limits presented here may exclude some exotic interpretations of the stochastic gravitational-wave background.