  We study local stability of the advection-dominated optically thick (slim)
and optically thin discs with purely toroidal magnetic field and the radial
viscous force using a linear perturbation analysis. Our dispersion relation
indicates that the presence of magnetic fields and radial viscous force cannot
give rise to any new mode of the instability. We find, however, that growth
rate of the thermal mode in the slim discs and that of the acoustic modes in
the slim and optically thin discs are dramatically affected by the radial
viscous force. This force tends to strongly decrease the growth rate of the
outward-propagating acoustic mode (O-mode) at the short-wavelength limit, but
it causes a slim disc to become thermally more unstable. We find that growth
rate of the thermal mode increases in the presence of radial viscous force.
This enhancement is more significant when the viscosity parameter is large. We
also show that growth rate of the O-mode reduces when radial viscous force is
considered. The growth rates of the thermal and acoustic modes depend on the
magnetic field. Although the instability of O-mode for a stronger magnetic
field case has a higher growth rate, the thermal mode of the slim discs can be
suppressed when the magnetic field is strong. The inertial-acoustic instability
of a magnetized disc may explain the quasi-periodic oscillations (QPOs) from
the black holes.
