Growth rate σ of the Tayler instability as a function of the solid-body rotation rate Ω_∥, in the p = 2 case. Normalized local growth rates are given for three different distances from the axis, σ(ϖ). The dashed line corresponds to the predicted growth rate of the Tayler instability for slow rotators, σ = ω_A,φ. The dotted-dashed line is the predicted behavior of the instability for fast rotators, .