Detecting the heterodyning of gravitational waves

Abstract: Gravitational waves modulate the apparent frequencies of other periodic signals. Low-frequency gravitational waves could therefore be detected by observing frequency modulations in signals from higher-frequency sources, e.g., those from binary white dwarfs detected with the LISA gravitational-wave detector. We propose a concrete method to extract these modulations by coherently adding the cross-spectra of a large number of well-resolved quasi-monochromatic signals. We apply this method to the case of LISA, and find this method would enable the detection of background gravitational wave strain amplitudes of, e.g., $A\simeq10^{-10}$ at a frequency $F\simeq10^{-8}\,\rm Hz$, given current projections for the number and properties of Galactic binary white dwarfs and the sensitivity of the instrument. We also estimate (to within an order of magnitude) that this method could potentially compete with that of current Pulsar Timing Arrays when using signals from binary neutron stars such as those expected to be observed with proposed detectors like DECIGO. Our results show that gravitational-wave detectors could be sensitive at frequencies outside of their designed bandwidth using the same infrastructure, which has the potential to open up unexplored and otherwise inaccessible parts of the gravitational wave spectrum.