Observing the Peculiar Acceleration of our Solar System with Quasar Proper Motions

Abstract: We measure the proper motion dipole of quasars observed by Gaia to determine the acceleration of the Solar System with respect to the quasar rest frame. We characterise the full angular power spectrum of the proper motion field using the pseudo-$C_\ell$ formalism and employ simulation-based inference to jointly constrain the dipole and higher multipole power. Cross-correlation with the Gaia scanning strategy, stellar density, and stellar proper motion maps is used to diagnose the origin of systematic power beyond the dipole. We apply this framework to both the Gaia EDR3 quasar catalogue and the Quaia catalogue. The inferred acceleration is consistent with the previous determination, but the credible intervals widen by factors of 1.5 to 2.5 when higher-multipole degeneracies are properly marginalised, indicating that previous uncertainty estimates were optimistic. Our best estimate, based on the Quaia catalogue is $$(g_x,\, g_y, \,g_z) =( 0.40^{{+0.70}<em>{-0.70},\,-5.09^{+0.54}</em>{-0.54},\,-2.40^{{+0.55}_{-0.58})}} \;μas \,yr<sup>{-1}$$, corresponding to an amplitude of $$5.72_{-0.52}^{+0.53}\,\rm μas\,yr<sup>{-1}$$. The acceleration shows no significant dependence on source redshift, providing further evidence for its kinematic origin.