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 { \Delta V } \equiv { \Omega _ { 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 { \Delta V } = 252 \pm 41 \mathrm { km } ~ { } \mathrm { s } ^ { -1 } , if u _ { LSR } = 0 .
Assuming further that R _ { 0 } = 8 kpc and V _ { LSR } = 220 \mathrm { km } ~ { } \mathrm { s } ^ { -1 } , this gives { \Omega _ { p } } = 59 \pm 5 \mathrm { km } ~ { } \mathrm { s } ^ { -1 } ~ { } \mathrm { kpc } ^ { -1 } with a possible systematic error of perhaps 10 \mathrm { km } ~ { } \mathrm { s } ^ { -1 } ~ { } \mathrm { kpc } ^ { -1 } .
The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG .