Magnetic instability in a differentially rotating star

Instabilities in magnetic fields wound up by differential rotation as reviewed in Spruit (1999) are discussed with some detail and new developments added. In stellar models which include magnetic torques, the differential rotation tends to accumulate in the gradients in composition. In view of this, instability in a $\mu$-gradient is studied in more detail here, resulting in the detection of a second instability. Its relevance for angular momentum transport is uncertain, however, since it requires high horizontal field gradients and would not operate near the pole. Finally, the possibility is discussed that magnetic instability in a $\mu$-gradient will lead to {\em layer formation}: the gradients breaking up into small steps of uniform composition and rotation rate. This would enhance the angular momentum transport across inhomogeneous zones, and decrease the rotation rates of the end products of stellar evolution. A recent {\tt astro-ph} submission by Dennisenkov and Pinsonneault proposing a modification of the instability conditions is shown to contain a mathematical error.