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The study of the magnetic field in stellar radiation zones is an importanttopic in modern astrophysics because the magnetic field can play an importantrole in several transport phenomena such as mixing and angular momentumtransport. We consider the influence of rotation on stability of apredominantly toroidal magnetic field in the radiation zone. We find that theeffect of rotation on the stability depends on the magnetic configuration ofthe basic state. If the toroidal field increases sufficiently rapidly with thespherical radius, the instability cannot be suppressed entirely even by a veryfast rotation although the strength of the instability can be significantlyreduced. On the other hand, if the field increases slowly enough with theradius or decreases, the instability has a threshold and can be completelysuppressed in rapidly rotating stars. We find that in the regions where theinstability is entirely suppressed a particular type of magnetohydrodynamicwaves may exist which are marginally stable.

Rotational suppression of the Tayler instability in stellar radiation zones