We present a theoretical model in order to explain the formation and the evolution of the molecular outflows associated to protostars. In this model, we assume that the molecular outflow is a thin shell formed by the interaction between a fast stellar wind and a rotating cloud envelope in gravitational collapse. We obtain a set of partial differential equations, these equations are space and time dependent, and describe the physical properties of the shell, e.g., the mass and momentum fluxes and the radius. We have done a study of the interaction between the rotating envelope studied by Ulrich (1976), and a stellar wind without rotation. We show an analysis from the dynamic standpoint and we consider both isotropic and anisotropic stellar winds. Of this model, we obtain the shape of the shell, the mass surface density, the velocity field, and the angular momentum of the material into the shell. We find that there is a critical value of the ratio between the wind and the accretion flow momentum rates β that allows the shell to expand. In this model, the rotation velocity of the shell is lower than the values measured in several sources. Finally, we compare this model with the observational data of the molecular outflow associated with the young star of Orion Source I. We present 29SiO(J=8–7) ν=0, SiS (J=19–18) ν=0, and SiO (J=8–7) ν=1 molecular line observations made with the Atacama Large Millimeter/Submillimeter Array (ALMA). From this comparison, we find that the values of the outer radius, the expansion velocity, and the opening angle show a similar behavior. However, the rotation velocity of the model is much more lower (3−10 times) than the observed velocity values in the outflow from Orion Source I.
Local contact: Guillem Anglada