Periodic instabilities in protostellar disks with azimuthal magnetic fields

The stability of magnetohydrodynamic oscillations in a protostellar disk with a toroidal magnetic field is analyzed. It is shown that, apart from the aperiodic magnetorotational instability, two other types of periodic instabilities of non-axisymmetric perturbations can exist. The simultaneous presence of azimuthal and vertical components of the wave vector are necessary for these to exist. One instability is due to the inductive winding-up of the azimuthal magnetic field of the wave, and the other arises when the field amplitude is increased by a comoving Hall wave, transferring magnetic field into a region of enhanced field intensity. The bandwidths of the unstable wave numbers are analyzed as a function of the Hall current, the beta parameter of a plasma, and the angle between the direction of wave propagation and the plane of the disk. Regions in the accretion disks typical of T Tauri stars are indentified where these instabilities could be most active.