Binary systems as resonance detectors for gravitational waves

Abstract

Gravitational waves at suitable frequencies can resonantly interact with a binary system, inducing changes to its orbit. A stochastic gravitational wave background causes the orbital elements of the binary to execute a classic random walk, with the variance of orbital elements growing with time. The lack of such a random walk in binaries that have been monitored with high precision over long time scales can thus be used to place an upper bound on the gravitational wave background. Using periastron time data from the Hulse-Taylor binary pulsar spanning $\ensuremath{\sim}30$ years, we obtain a bound of ${h}_{\mathrm{c}}<7.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$ at $\ensuremath{\sim}{10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{Hz}$, where ${h}_{\mathrm{c}}$ is the strain amplitude per logarithmic frequency interval. Our constraint complements those from pulsar timing arrays, which probe much lower frequencies, and ground-based gravitational wave observations, which probe much higher frequencies. Interesting sources in our frequency band, which overlaps the lower sensitive frequencies of proposed space-based observatories, include white dwarf/supermassive black hole binaries in the early/late stages of inspiral, and TeV-scale preheating or phase transitions. The bound improves as $(\mathrm{\text{time span}}{)}^{\ensuremath{-}2}$ and $(\mathrm{\text{sampling rate}}{)}^{\ensuremath{-}1/2}$. The Hulse-Taylor constraint can be improved to $\ensuremath{\sim}3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}15}$ with a suitable observational campaign over the next decade. Our approach can also be applied to other binaries, including (with suitable care) the Earth-Moon system, to obtain constraints at different frequencies. The observation of additional binary pulsars with the Square Kilometer Array could reach a sensitivity of ${h}_{\mathrm{c}}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$.