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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mi>h</mml:mi> <mml:mn>70</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> <mml:msub> <mml:mo>Ω</mml:mo> <mml:mi>GW</mml:mi> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>0.023</mml:mn> </mml:math> (95% confidence limit), for frequencies between 11.2 nHz and 3.1 × 10 −9 nHz (1.33/ t 0 ). 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 h c ≤ 2.7 × 10 −12 for f ref = 1 yr −1 and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mi>h</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>70</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msubsup> <mml:msub> <mml:mrow> <mml:mo mathvariant="normal">Ω</mml:mo> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">GW</mml:mi> </mml:mrow> </mml:msub> <mml:mo>≤</mml:mo> <mml:mn>0.0096</mml:mn> </mml:math> at 95% confidence. We probe down to ±0.005 μ as 2 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.