  The strength and direction of migration of embedded low mass planets depends
on the disc's structure. It has been shown that, in discs with viscous heating
and radiative transport, the migration can be directed outwards. In this paper
we investigate the influence of a constant dM/dt-flux through the disc, as well
as the influence of the disc's metallicity on the disc's thermodynamics. We
focus on dM/dt discs, which have a net mass flux through them. Utilizing the
resulting disc structure, we determine the regions of outward migration in the
disc. We perform numerical hydrosimulations of dM/dt discs with viscous
heating, radiative cooling and stellar irradiation in 2D in the r-z-plane. We
use the explicit/implicit hydrodynamical code FARGOCA 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 of embedded planets is studied by using torque formulae. For a
disc of gas surface density and viscosity, we find that the discs thermal
structure depends on the product Sigma_G \nu and the amount of heavy elements,
while the migration of planets additionally to the mentioned quantities,
depends on the amount of viscosity itself. As a result of this, the disc
structure can not be approximated by simple power laws. During the lifetime of
the disc, the structure of the disc changes significantly in a non-linear way
in the inner parts. In the late stages of the discs evolution, outward
migration is only possible if the metallicity of the disc is high. For low
metallicity, planets would migrate inwards and could potentially be lost. The
presented disc structures and migration maps have important consequences on the
formation of planets, as they can give hints on the different formation
mechanisms for different types of planets as a function of metallicity.
