# Angular momentum in bipolar outflows: dynamical evolutionary model

## TL;DR

This paper presents a dynamical model of bipolar molecular outflows driven by stellar winds interacting with rotating collapsing clouds, analyzing shell shapes, velocities, and angular momentum evolution.

## Contribution

It introduces a time-dependent, numerical model of bipolar outflows considering wind anisotropy and rotation, providing new insights into shell dynamics and angular momentum transfer.

## Key findings

- Shell elongation increases with wind anisotropy.
- Rotation velocities are lower than observed in some sources.
- A critical wind-to-accretion momentum ratio determines shell expansion.

## Abstract

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.