A ballistic bow shock model for jet-driven protostellar outflow shells

We analyze the dynamics of the shell produced when a bow shock from a collimated jet propagates into the surrounding medium. Under interstellar conditions, the shock is radiative, and a ballistic approximation for the shell flow is appropriate beyond the working surface where the jet impacts its surroundings. The solution is then determined by the ambient and jet densities and velocities and by the momentum impulse applied in the working surface. Using estimates for these impulses (confirmed by separate numerical simulations), we obtain solutions for the shell structure, and for the range of velocities in the shell at any point. We provide predictions for the position-velocity and mass-velocity relations expected for plane-of-sky bow-shock shells, and for the bulk shell properties. In a companion paper, we show that these analytic solutions are in excellent agreement with the results of direct numerical simulations. We argue that classical molecular (CO) outflows cannot be purely jet-driven, because the bow-shock shell solutions are much too elongated compared with observations. Finally, we suggest that the ``spur'' structures seen in position-velocity diagrams of observed molecular outflows are the manifestation of internal bow shocks which may be fit with our simple dynamical models.