The mean Galactocentric radial velocities \langle v _ { R } \rangle ( R, \phi ) of luminous red giant stars within the mid-plane of the Milky Way reveal a spiral signature , which could plausibly reflect the response to a non-axisymmetric perturbation of the gravitational potential in the Galactic disk .
We apply a simple steady-state toy model of a logarithmic spiral to interpret these observations , and find a good qualitative and quantitative match .
Presuming that the amplitude of the gravitational potential perturbation is proportionate to that in the disk ’ s surface mass density , we estimate the surface mass density amplitude to be \Sigma _ { max } ( R _ { \odot } ) = 14 \pm 5 M _ { \odot } pc ^ { -2 } at the solar radius .
Combined with the local disk density , this implies a surface mass density contrast between the arm and inter-arm regions of approximately \pm 20 \% at the solar radius , with an increase towards larger Galactocentric radii .
Our model constrains the pitch angle of the dynamical spiral arms to be 12.7 ^ { \circ } \pm 1.2 ^ { \circ } .