The Pattern Speed of the OH/IR Stars in the Milky Way

Abstract

We show how the continuity equation can be used to determine pattern speeds in the Milky Way Galaxy (MWG). This method, first discussed by Tremaine & Weinberg in the context of external galaxies, requires projected positions, $(l,b)$, and line-of-sight velocities for a spatially complete sample of relaxed tracers. If the local standard of rest (LSR) has a zero velocity in the radial direction ($u_{\rm LSR}$), then the quantity that is measured is $\Delta V \equiv \Omega_p R_0 - V_{\rm LSR}$, where $\Omega_p$ is the pattern speed of the non-axisymmetric feature, $R_0$ is the distance of the Sun from the Galactic centre and $V_{\rm LSR}$ is the tangential motion of the LSR, including the circular velocity. We use simple models to assess the reliability of the method for measuring a single, constant pattern speed of either a bar or spiral in the inner MWG. We then apply the method to the OH/IR stars in the ATCA/VLA OH 1612 MHz survey of Sevenster et al, finding $\Delta V = 252 \pm 41$ km/s, if $u_{\rm LSR} = 0$. Assuming further that $R_0 = 8$ kpc and $V_{\rm LSR} = 220$ \kms, this gives $\Omega_p = 59\pm 5$ km/s/kpc with a possible systematic error of perhaps 10 km/s/kpc. The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG.