The pattern speed of the OH/IR stars in the Milky Way

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 DeltaV equivalent toOmega (p) R (0) - V (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 (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 DeltaV =252+/-41 km s (-1), if u (LSR)=0. Assuming further that R (0) =8 kpc and V (LSR) =220 km s(-1), this gives Omega(p) =59+/-5 km s(-1) kpc(-1) with a possible systematic error of perhaps 10 km s(-1)kpc(-1). The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG.