Power spectrum of longitudinal-velocity residuals in the Galactic disk from Gaia DR3 red-giant-branch stars

Non-axisymmetric structures in the Galaxy produce coherent stellar motions in the Galactic disk. These motions are usually interpreted by assuming parameterized gravitational potentials or specific perturbation models, thereby entangling direct kinematic information with model-dependent assumptions. Using Gaia DR3 astrometry, we analyze the Galactic longitudinal-velocity residuals of nearly four million red-giant-branch stars over $-4 < X_h < 4\, \mathrm{kpc}$ and $-6 < Y_h < 6\, \mathrm{kpc}$ in the heliocentric region. We construct an empirical axisymmetric baseline without introducing any dynamical model, and compute the power spectrum of the residual velocity field. The spectrum exhibits a broad peak at spatial frequency of $f \simeq 0.12 - 0.22\, \mathrm{kpc}^{-1}$, corresponding to a scale of around $5-8\, \mathrm{kpc}$. The residual amplitude is sensitive to the adopted distance scale: inverse-parallax distances $d_\varpi$ yield a peak of around $16\, \mathrm{km\, s^{-1}}$, while the Bailer-Jones geometric distances $r_{\mathrm{geo}}$ yield around $12\, \mathrm{km\, s^{-1}}$. Minimizing the low-frequency power favors a solar radial motion of $U_\odot=10.8\, \mathrm{km\, s^{-1}}$ based on $d_\varpi$ and $U_\odot=10.4\, \mathrm{km\, s^{-1}}$ based on $r_{\mathrm{geo}}$. Collectively, the resulting spectrum establishes Gaia astrometry as a direct probe of disk-wide non-axisymmetric kinematics and provides quantitative targets for future dynamical modeling and interpretation.