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 } \mathrm { km s } ^ { -1 } \mathrm { kpc } ^ { -1 } and a small amplitude A = 0.55 ^ { +0.02 } _ { -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 .