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 _ { 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 .