  Hydrodynamical instabilities in disks around young stars depend on the
thermodynamic stratification of the disk and on the local rate of thermal
relaxation. Here, we map the spatial extent of unstable regions for the
Vertical Shear Instability (VSI), the Convective OverStability (COS), and the
amplification of vortices via the Subcritical Baroclinic Instability (SBI). We
use steady state accretion disk models, including stellar irradiation,
accretion heating and radiative transfer. We determine the local radial and
vertical stratification and thermal relaxation rate in the disk, in dependence
of the stellar mass, disk mass and mass accretion rate. We find that passive
regions of disks - i.e. the midplane temperature dominated by irradiation - are
COS unstable about one pressure scale height above the midplane and VSI
unstable at radii $> 10 \, \text{au}$. Vortex amplification via SBI should
operate in most parts of active and passive disks. For active parts of disks
(midplane temperature determined by accretion power) COS can become active down
to the midplane. Same is true for the VSI because of the vertically adiabatic
stratification of an internally heated disk. If hydro instabilities or other
non-ideal MHD processes are able to create $\alpha$-stresses ($> 10^{-5}$) and
released accretion energy leads to internal heating of the disk, hydrodynamical
instabilities are likely to operate in significant parts of the planet forming
zones in disks around young stars, driving gas accretion and flow structure
formation. Thus hydro-instabilities are viable candidates to explain the rings
and vortices observed with ALMA and VLT.
