2002MNRAS.334..355D

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_LSR), then the quantity that is measured is ΔV≡Ω_pR₀-V_LSR, where Ω_p is the pattern speed of the non-axisymmetric feature, R₀ is the distance of the Sun from the Galactic centre and V_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 ΔV =252±41km.s^–1, if u_LSR=0. Assuming further that R₀=8kpc and V_LSR=220km.s^–1, this gives Ω_p=59±5km.s^–1.kpc^–1 with a possible systematic error of perhaps 10km.s^–1.kpc^–1. The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG.