A semi-analytical model of the outer structure of protoplanetary discs formed by the collapse of a rotating molecular cloud

Context. Protoplanetary discs are formed as a result of the fragmentation and collapse of giant molecular cloud cores. The physical properties and structure of a formed disc are of great importance in studies of the onset of planet formation processes. Aims. Starting from the isothermal collapse of a rotating Bonnor–Ebert sphere and assuming the conservation of angular momentum, we have looked for the structure equations of the newly formed protoplanetary disc. We take into account the possible role of pressure gradient in forming the initial disc structure and compare our results with those obtained from a ‘Keplerian’ infall model. Our aim is to obtain the initial conditions to numerically study the evolution of the gaseous and solid components of protoplanetary discs. Methods. The structure equations developed for protoplanetary discs were derived analytically, while the equations were solved numerically. Results. The surface density profiles of the newly formed protoplanetary discs strongly depend on the initial rotation state of the Bonnor–Ebert sphere. According to our results, for slow rotators, gravitational instabilities can develop in the early phases of disc formation. However, for relatively fast rotators, the outermost regions of the resulting discs are gravitationally stable, quite massive, and highly sub-Keplerian, allowing for rapid dust transport to the inner disc and fueling subsequent planet formation.