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

Abstract

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, (95% confidence limit), for frequencies between 11.2 nHz and 3.1 × 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 × 10−12 for fref = 1 yr−1 and at 95% confidence. We probe down to ±0.005 μas2 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 ∼1 nHz for massive black hole binaries. The limits presented here may exclude some exotic interpretations of the stochastic gravitational-wave background.