  Context: Several recent studies have found that planet migration in adiabatic
discs differs significantly from migration in isothermal discs. Depending on
the thermodynamic conditions, i.e., the effectiveness of radiative cooling, and
the radial surface density profile, planets migrate inward or outward. Clearly,
this will influence the semimajor axis - mass distribution of planets as
predicted by population synthesis simulations. Aims: Our goal is to study the
global effects of radiative cooling, viscous torque desaturation and gap
opening as well as stellar irradiation on the tidal migration of a synthetic
planet population. Methods: We combine results from several analytical studies
and 3D hydrodynamic simulations in a new semi-analytical migration model for
the application in our planet population synthesis calculations. Results: We
find a good agreement of our model with torques obtained in a 3D radiative
hydrodynamic simulations. We find three convergence zones in a typical disc,
towards which planets migrate from the in- and outside, affecting strongly the
migration behavior of low-mass planets. Interestingly, this leads to slow type
II like migration behavior for low-mass planets captured in those zones even
without an ad hoc migration rate reduction factor or a yet to be defined
halting mechanism. This means that the new prescription of migration including
non-isothermal effects makes the preciously widely used artificial migration
rate reduction factor obsolete. Conclusions: Outward migration in parts of a
disc makes some planets survive long enough to become massive. The convergence
zones lead to a potentially observable accumulations of low-mass planets at
certain semimajor axes. Our results indicate that further studies of the mass
where the corotation torque saturates will be needed since its value has a
major impact on the properties of planet populations.
