We model molecular outflows produced by the time dependent interaction between a stellar wind and a rotating cloud envelope in gravitational collapse, studied by Ulrich. We consider spherical and anisotropic stellar winds. We assume that the bipolar outflow is a thin shocked shell, with axial symmetry around the cloud rotation axis and obtain the mass and momentum fluxes into the shell. We solve numerically a set of partial differential equations in space and time, and obtain the shape of the shell, the mass surface density, the velocity field, and the angular momentum of the material in the shell. We find that there is a critical value of the ratio between the wind and the accretion flow momentum rates $beta$ that allows the shell to expand. As expected, the elongation of the shells increase with the stellar wind anisotropy. In our models, the rotation velocity of the shell is the order to 0.1 - 0.2 km s$^{-1}$, a factor of 5-10 lower than the values measured in several sources. We compare our models with those of Wilkin and Stahler for early evolutionary times and find that our shells have the same sizes at the pole, although we use different boundary conditions at the equator.
Download