The structure of protoplanetary discs around evolving young stars
  The formation of planets with gaseous envelopes takes place in protoplanetary accretion discs on time-scales of several millions of years. Small dust particles stick to each other to form pebbles, pebbles concentrate in the turbulent flow to form planetesimals and planetary embryos and grow to planets, which undergo substantial radial migration. All these processes are influenced by the underlying structure of the protoplanetary disc, specifically the profiles of temperature, gas scale height and density. The commonly used disc structure of the Minimum Mass Solar Nebular (MMSN) is a simple power law in all these quantities. However, protoplanetary disc models with both viscous and stellar heating show several bumps and dips in temperature, scale height and density caused by transitions in opacity, which are missing in the MMSN model. These play an important role in the formation of planets, as they can act as sweet spots for the formation of planetesimals via the streaming instability and affect the direction and magnitude of type-I-migration. We present 2D simulations of accretion discs that feature radiative cooling, viscous and stellar heating, and are linked to the observed evolutionary stages of protoplanetary discs and their host stars. These models allow us to identify preferred planetesimal and planet formation regions in the protoplanetary disc as a function of the disc's metallicity, accretion rate and lifetime. We derive simple fitting formulae that feature all structural characteristics of protoplanetary discs during the evolution of several Myr. These fits are straightforward to apply for modelling any growth stage of planets where detailed knowledge of the underlying disc structure is required. 
Bertram Bitsch, Anders Johansen, Michiel Lambrechts and Alessandro   Morbidelli
astro-ph.EP