A Plausible Galactic Spiral Pattern and its Rotation Speed

We report calculations of the stellar and gaseous response to a Milky Way mass distribution model including a spiral pattern with a locus as traced by K-band observations, over imposed on the axisymmetric components in the plane of the disk. The stellar study extends calculations from previous work concerning the self-consistency of the pattern. The stellar response to the imposed spiral mass is studied via computations of the central family of periodic and nearby orbits as a function of the pattern rotation speed, $\Omega_p$, among other parameters. A fine grid of values of $\Omega_p$ was explored ranging from 12 to 25 $km s^{-1} kpc^{-1}$. Dynamical self-consistency is highly sensitive to $\Omega_p$, with the best fit appearing at 20 $km s^{-1} kpc^{-1}$. We give an account of recent independent pieces of theoretical and observational work that are dependent on the value of $\Omega_p$, all of which are consistent with the value found here; the recent star formation history of the Milky Way, local inferences of cosmic ray flux variations and Galactic abundance patterns. The gaseous response, which is also a function of $\Omega_p$, was calculated via 2D hydrodynamic simulations with the ZEUS code. For $\Omega_p = 20 km s^{-1} kpc^{-1}$, the response to a two-armed pattern is a structured pattern of 4 arms, with bifurcations along the arms and interarm features. The pattern resembles qualitatively the optical arms observed in our Galaxy and other galaxies. The complex gaseous pattern appears to be linked to resonances in stellar orbits. Among these, the 4:1 resonance plays an important role, as it also determines the extent over which the imposed spiral pattern is dynamically self-consistent.