Probing the Kinematic Dipole with LISA: an analytical treatment

The motion of the Solar System with respect to the cosmic rest frame induces a kinematic dipole in the stochastic gravitational-wave background (GWB). Detecting this signal with space-based interferometers would provide an independent measurement of our peculiar velocity and a GW probe of cosmic anisotropies. We present a fully analytic derivation of the response of the \emph{Laser Interferometer Space Antenna} (LISA) to a kinematic dipole, and construct an optimal estimator for its detection. We show that the dipolar response is governed by a single frequency-dependent function fixed by symmetry, and we compute its behaviour across the LISA band. Using Fisher forecasts, we find that for a scale-invariant background detectability requires $h^2\Omega_{\rm GW} \gtrsim 5\times 10^{-8}$ for \emph{fiducial} LISA, and $h^2\Omega_{\rm GW} \gtrsim 5\times 10^{-10}$ for a detector with characteristic instrumental-noise amplitudes improved by an order of magnitude. Prospects are more favorable for signals with richer frequency profile. We also explore the potential of the kinematic dipole to break degeneracies, particularly in the presence of strong galactic foregrounds or noise features that closely mimic the primordial signal.