Detecting gravitomagnetism with space-based gravitational wave observatories

We discuss the idea of a measurement that, making use of data from space interferometers, could detect the gravito-magnetic field generated by the rotation of the Milky Way, including the possible contribution of the dark matter halo. The galactic signal would be superposed to the gravito-magnetic field of the Sun. The proposed technique is based on the asymmetric propagation of light along the closed contour of the space interferometer, in a Sagnac-like approach. We discuss the principles of detection as well as some practical aspects of the proposed experiment using, as a case study, LISA, the most mature project to date. Both gravito-magnetic signals will be modulated thanks to the annual oscillation of the plane of the interferometer with respect to the galactic plane and to the spin axis of the Sun. Although larger than the detector intrinsic noise, these signals will be superposed to a much larger kinematic modulation due to orbital motion, making them very hard to be observed. We also mention a second phenomenon, where the gravito-magnetic field rotates the polarization of the propagating electromagnetic beams: the effect will be present in LISA, although exceedingly small and out of reach of present technology