Contour map of the minimal eigenvalue ﹩{\tilde{\omega }}_{\min }^{2}﹩, plotted across the β-q plane for an azimuthal wavenumber m = 1 and equilibrium models having γ = 5/3. Regions where ﹩{\tilde{\omega }}_{\min }^{2}\lt 0﹩ are unstable to the Tayler instability. The three black lines show the stability boundaries for the fully compressible criteria (TI), the constrained anelastic criteria (cTI) and the LBR anelastic criteria (anTI). Only the LBR anelastic criteria correctly predict the ﹩{\tilde{\omega }}_{\min }^{2}=0﹩ stability boundary.