Instabilities of MHD Waves Produced by Coupling of Rotation and Gradient   of Magnetic Field and its Possible Application in the Galactic Central Region
  An analysis of MHD wave propagating in a gravitating and rotating medium permeated by non-uniform magnetic field has been done. It has been found that the Gradient of Magnetic Field when coupled with Rotation becomes capable to generate few instabilities (Temporal or Spatial) leading to the damping or amplification of MHD waves. The Jean's criterion is not sufficient for stability always. Rather, the waves will suffer instability unless their wave length (frequency) is less (greater) than certain critical values. Otherwise, those will smoothly propagate outward. Out of different scenarioes depending on the direction of the magnetic field, its gradient, rotation and wave propagation three important Special Cases have been discussed and different stability criteria have been derived.   Finally, using the above theory we have obtained the stability/instability criteria for the waves moving parallel and perpendicular to the galactic plane in the Core and Periphery of the Central Region of Galaxy (C.R.G.) due to the coupled action of Rotation and Non-Uniform Magnetic field. The possibility of heating or occuring diffused condition inside the central region by MHD waves or smooth propagation of these waves (under some restrictions) through the C.R.G. has been briefly discussed. The numerical values of the parameters of those waves for instabilities or smooth propagation have been estimated roughly. One may find some clues for the formation of Halo and Spiral Arms. 
Ipsita Das and Ramaprosad Bondyopadhaya