Protoplanetary accretion disc models: The effects of several meteoritic, astronomical, and physical constraints
The concept of a protosolar viscous accretion disc is reviewed and a simple accretion disc model is laid out in such a way that the parameters controlling the properties and evolution of the disc can be varied easily. This model is used to assess the effects produced by four possible constraints on the solar nebula that have been widely discussed: a "planet formation" constraint, set by the time scale of the growth of giant planets, a "meteoritic" constraint that temperatures in what is now the asteroid belt must have been high enough to melt and vaporize silicates (˜1500° K), an "astronomical" constraint that the accretion rate of interstellar material onto protostellar discs had to be high (˜10 -4solar mass/year) to account for the age-luminosity properties of T-Tauri stars in the Hertzsprung-Russell diagram, and a "physical" constraint that the speed of gas turbulence in discs dominated by convective instability is small (Mach number ˜10 -3). We find that all four constraints cannot be accomodated simultaneously, in particular the physical constraint causes difficulties. The resulting discs formed during the accretion stage (when collapsing interstellar material is being added) are too small compared with our planetary system. We conclude that planet formation occured predominantly during a phase of disc evolution after infall ceased, during which viscous transfer of angular momentum caused the disc to expand in radius as it cooled. Combining the planet formation constraint, in particular, with the others, gives us a range of allowed parameters of viable disc models.