Steady Wind-Blown Cavities within Infalling Rotating Envelopes:
  Application to the Broad Velocity Component in Young Protostars
  Wind-driven outflows are observed around a broad range of accreting objects
throughout the Universe, ranging from forming low-mass stars to super-massive
black holes. We study the interaction between a central isotropic wind and an
infalling, rotating, envelope, determining the steady-state cavity shape formed
at their interface under the assumption of weak mixing. The shape of the
resulting wind-blown cavity is elongated and self-similar, with a physical size
determined by the ratio between wind ram pressure and envelope thermal
pressure. We compute the growth of a warm turbulent mixing-layer between the
shocked wind and the deflected envelope, and calculate the resultant broad line
profile, under the assumption of a linear (Couette-type) velocity profile
across the layer. We then test our model against the warm broad velocity
component observed in CO $J$=16--15 by Herschel/HIFI in the protostar
Serpens-Main SMM1. Given independent observational constraints on the
temperature and density of the dust envelope around SMM1, we find an excellent
match to all its observed properties (line profile, momentum, temperature) and
to the SMM1 outflow cavity width for a physically reasonable set of parameters:
a ratio of wind to infall mass-flux $\simeq 4\%$, a wind speed $v_{\rm w}
\simeq 30$ km/s, an interstellar abundance of CO and H$_2$, and a turbulent
entrainment efficiency consistent with laboratory experiments. The inferred
ratio of ejection to disk accretion rate, $\simeq 6-20\%$, is in agreement with
current disk wind theories. Thus, the model provides a new framework to
reconcile the modest outflow cavity widths in protostars with the large
observed flow velocities. Being self-similar, it is applicable over a broader
range of astrophysical contexts as well.
