Graviton mass from close white dwarf binaries detectable with LISA

Abstract

The arrival times of gravitational waves and optical light from orbiting binaries provide a mechanism to understand the propagation speed of gravity when compared to that of light or electromagnetic radiation. This is achieved with a measurement of any offset between the optically derived orbital phase and that derived from gravitational wave data, at a specified location of one binary component with respect to the other. Using a sample of close white dwarf binaries (CWDBs) detectable with the Laser Interferometer Space Antenna and optical light curve data related to binary eclipses from meter-class telescopes for the same sample, we determine the accuracy to which orbital phase differences can be extracted. We consider an application of these measurements involving a variation of the speed of gravity, when compared to the speed of light, due to a massive graviton. For a subsample of $\ensuremath{\sim}400$ CWDBs with high signal-to-noise ratio gravitational wave and optical data with magnitudes brighter than 25, the combined upper limit on the graviton mass is at the level of $\ensuremath{\sim}6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}\mathrm{eV}.$ This limit is two orders of magnitude better than the present limit derived by Yukawa-correction arguments related to the Newtonian potential and applied to the Solar System.