  The strength and direction of migration of low mass planets depends on the
disc's thermodynamics. In discs where the viscous heating is balanced by
radiative transport, the migration can be directed outwards, a process which
extends the lifetime of growing planetary embryos. We investigate the influence
of opacity and stellar irradiation on the disc thermodynamics. Utilizing the
resulting disc structure, we determine the regions of outward migration. We
perform two-dimensional numerical simulations of equilibrium discs with viscous
heating, radiative cooling and stellar irradiation. We use the hydrodynamical
code NIRVANA that includes a full tensor viscosity and stellar irradiation, as
well as a two temperature solver that includes radiation transport in the
flux-limited diffusion approximation. The migration is studied by using torque
formulae. In the constant opacity case, we reproduce the analytical results of
a black-body disc: the stellar irradiation dominates in the outer regions --
leading to flaring -- while the viscous heating dominates close to the star. We
find that the inner edge of the disc should not be significantly puffed-up by
the stellar irradiation. If the opacity depends on the local density and
temperature, the structure of the disc is different, and several bumps in the
aspect ratio H/r appear, due to transitions between different opacity regimes.
The bumps in the disc can shield the outer disc from stellar irradiation.
Stellar irradiation is an important factor for determining the disc structure
and has dramatic consequences for the migration of embedded planets. Compared
to discs with only viscous heating, a stellar irradiated disc features a much
smaller region of outward migration for a range of planetary masses. This
suggests that the region where the formation of giant planet cores takes place
is smaller, which in turn might lead to a shorter growth phase.
