The properties of the local spiral arms from RAVE data: two-dimensional density wave approach

Using the RAVE survey, we recently brought to light a gradient in the mean galactocentric radial velocity of stars in the extended solar neighbourhood. This gradient likely originates from non-axisymmetric perturbations of the potential, among which a perturbation by spiral arms is a possible explanation. Here, we apply the traditional density wave theory and analytically model the radial component of the two-dimensional velocity field. Provided that the radial velocity gradient is caused by relatively long-lived spiral arms that can affect stars substantially above the plane, this analytic model provides new independent estimates for the parameters of the Milky Way spiral structure. Our analysis favours a two-armed perturbation with the Sun close to the inner ultra-harmonic 4:1 resonance, with a pattern speed \Omega_p=18.6^{+0.3}_{-0.2} km/s/kpc and a small amplitude A=0.55 \pm 0.02% of the background potential (14% of the background density). This model can serve as a basis for numerical simulations in three dimensions, additionally including a possible influence of the galactic bar and/or other non-axisymmetric modes.