The Strength of the Dynamical Spiral Perturbation in the Galactic Disk

The mean Galactocentric radial velocities $\langle v_{R}\rangle(R,\varphi)$ 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 $\Sigma_{\rm max} (R_{\odot})\approx 5.5\,\rm M_{\odot}\,pc^{-2}$ at the solar radius when choosing a fixed pattern speed of $\Omega_{\mathrm p}=12\,\rm km\,s^{-1}\,kpc^{-1}$. Combined with the local disk density, this implies a surface mass density contrast between the arm and inter-arm regions of approximately $\pm 10\%$ at the solar radius, with an increases towards larger radii. Our model constrains the pitch angle of the dynamical spiral arms to be approximately $12^{\circ}$.