The stability of magnetized protostellar disks with the Hall effect and buoyancy

The stability properties of cool protostellar disks are examined by use of the dispersion relation taking into account the Hall effect and buoyancy. Depending on the conditions, different types of instabilities can arise in different regions of the disk. In very low-ionized regions the instability associated with baroclinic effects of buoyancy is likely most efficient. The shear-Hall instability will be responsible for destabilization of regions with a weak magnetic field (parallel to the rotation axis) and with low conductivity (${\rm \Lambda}<a_{\rm e}$, ${\rm \Lambda}=\sigma B^2/\rho\Omega$ Elsässer number, ae magnetization parameter of electrons). The magnetorotational instability modified by buoyancy should be the main destabilizing factor in regions with sufficiently strong magnetic fields and/or high conductivity (${\rm \Lambda} > a_{\rm e}$). For a magnetic field amplitude of 1 Gauss the transition between both the regions happens at approximately 1 AU