Open Access

Rolf Ebert

• In this paper an instability calculation is given for an axially symmetric gas distribution which has a differential rotation and in which a magnetic field is present. It is a generalization of similar calculations given by CHANDRASEKHAR and BEL and SCHATZMAN. The generalization becomes necessary for the study of problems of the formation of planetary systems, and star formation. The instability conditions and the critical wave lengths are calculated for plane-wave-like disturbances. For disturbances running perpendicularly to the axis of rotation instability can occur only if the gas density exceeds a critical value which depends on the differential rotation at the considered distance only as long as pressure gradients and gradients of the magnetic field strength are negligible. If the gas density exceeds this critical value the shortest unstable wave length is proportional to the square root of vT2+vB2, where vT means the velocity of sound and vB the ALFVÉN-velocity. For disturbances running parallel to the axis of rotation in addition to the JEANS instability a new type of instability occurs due to the simultaneous action of the magnetic field and the differential rotation; for rigid rotation this instability vanishes.