  The collapse of interstellar gaseous clouds towards a protostar leads to the
formation of accretion disks around the central star. Such disks can be
dynamically stable if they settle in an axisymmetric state. In this letter, we
investigate the long-term stability of astrophysical viscous disks around
various protostars. We apply an implicit numerical code which solves the
equations of radiation hydrodynamics and treats turbulence-induced viscosity
according to the $\alpha$-viscosity model. We show how the viscosity is related
to the disk mass. A stability criterion to determine the maximum disk mass can
be formulated. We analyse such instabilities for a variety of radial points
with different orbital distances from the host star and discuss the feedback on
the disk in the event of an unstable protoplanetary disk. Additionally, we
examine the critical disk-mass for disks with variable outer boundaries and
compare them to observations of protostellar disks in the Upper Scorpius OB
Association and near the Lupus complex. We derive an easily applicable method
to obtain an estimate for maximum disk masses when the outer disk radius ins
known.
