We constrain the dynamical perturbations of the spiral arms in the Milky Way disk, based on the non-axisymmetric streaming motions of RGB stars revealed by APOGEE and gaia. We developed a revised steady-state radial-velocity response model that incorporates both the šin and the dynamically important čos components for a two-armed logarithmic spiral potential. The model was validated using orbit integrations with and Bayesian parameter recovery with, and was applied to the smoothed two-dimensional radial-velocity field of RGB stars while accounting for Lindblad and corotation resonances. AGAMA dynesty The revised model reproduces the phase and amplitude of the mock radial-velocity field to the sim2% level, substantially improving upon earlier šin-only formulations. Applied to the observational data, it yields a robust pitch angle of p ≃ 10^̧irc and a local surface density contrast of ξ ≃ 5--18% at the solar radius. The radial scale length is less well constrained (hr ≃ 40--50̨pc) due to intrinsic parameter covariance. Resonance effects strongly shape the velocity field, affecting the fitting: the radial velocity becomes extremely large near the Lindblad resonances, whereas it vanishes close to the corotation resonance. Our results demonstrate that including both the šin and čos terms is essential for a physically consistent interpretation of stellar streaming motions induced by a spiral potential. The observed kinematics constrain the spiral pattern speed to op ≈ 10--20̨mskpc.
Tang et al. (Tue,) studied this question.