The formation and evolution of protostellar discs; three-dimensional adaptive mesh refinement hydrosimulations of collapsing, rotating Bonnor-Ebert spheres

We present a detailed study of the collapse of molecular cloud cores using high-resolution three-dimensional adaptive mesh refinement (AMR) numerical simulations. In this first in a series of investigations our initial conditions consist of a spherical molecular core obeying the hydrostatic Bonnor-Ebert profile with varying degrees of initial rotation. Our simulations cover both the formation of massive discs, in which massive stars form, and low-mass discs. We use a customized version of the FLASH code the AMR technique, which allows us to follow the formation of a protostellar disc and protostellar core(s) through more than 10 orders in density increase, while continuously resolving the local Jeans length (i.e. obeying the Truelove criterion). Our numerical simulations also incorporate the energy loss due to molecular line emission in order to obtain a more realistic picture of the protostellar core and disc formation. Our initial states model systems of mass 168 and 2.1 M-circle dot that will form high- and low-mass stars, respectively. We follow many features such as the development complex shock structures, and the fragmentation of the disc. We find that slowly rotating cores (Omega t(ff) = 0.1) produce discs in which a strong bar develops but does not fragment. Faster initial rotation rates (Omega t(ff) = 0.2) result in the formation of a ring, which may fragment into two protostellar cores. The size of the rings found in our simulated discs agree with the observations of similar systems.