Probing Kinematic Anisotropies in the Stochastic Gravitational Wave Background with the SKA

Pulsar Timing Arrays (PTAs) and astrometric surveys provide complementary probes of the nanohertz stochastic gravitational-wave background (SGWB). A primary target is the kinematic dipole induced by the Solar System’s motion, whose detection would confirm the SGWB’s cosmological origin. We forecast the sensitivity of the Square Kilometre Array Observatory (SKAO) using optimal estimators and Fisher techniques, considering both the baseline AA4 configuration and an optimistic 1000 pulsar scenario, including the potential gain from combining with Gaia-like astrometry. While SKAO will substantially improve constraints on SGWB anisotropies, even joint analyses remain below the sensitivity required to detect the kinematic dipole, motivating new observational and analysis strategies to fully exploit this signal.