The linear hydromagnetic stability of inviscid compressible annular flows with magnetic Mach number \(M_{mag}<<1\) , corresponding to weak compressibility and a strong azimuthal magnetic field, is studied with respect to the class of near neutral magneto-subsonic axisymmetric normal modes. The method of integral relations is used to obtain general analytical results that give instability regions and growth rate estimates for unstable modes. For basic flows with positive minimum Richardson number \({\tilde{J}}_{m}\) it is shown that a necessary condition for instability is that \({\tilde{J}}_{m}\) is small. For unstable flows a semielliptical instability region depending on \({\tilde{J}}_{m}\) is obtained and this is further improved to get semielliptical-type regions depending on the wave number of the disturbance and the width of the annular channel. It is shown further that the growth rate of an arbitrary unstable mode is bounded and growth rate bounds depending on \({\tilde{J}}_{m}\) and width of the channel are given. It follows that the growth rate becomes small as the width of the annulus becomes small.
