Trapped Protostellar Winds and Their Breakout

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Observations show that high-velocity jets stem from deeply embedded young stars, which may still be experiencing infall from their parent cloud cores. Yet theory predicts that, early in this buildup, any outgoing wind is trapped by incoming material of low angular momentum. As collapse continues and brings in more rapidly rotating gas, the wind can eventually break out. Here we model this transition by following the motion of the shocked shell created by impact of the wind and a rotating, collapsing envelope. We first demonstrate, both analytically and numerically, that our previous, quasi-static solutions are dynamically unstable. Our present, fully time-dependent calculations include cases both where the wind is driven back by infall to the stellar surface and where it erupts as a true outflow. For the latter, we find that the time of breakout is 5 × 104 yr for wind speeds of 200 km s-1. The reason for the delay is that the shocked material, including the swept-up infall, must be able to climb out of the star's gravitational potential well. We explore the critical wind speed necessary for breakout as a function of the mass transport rates in the wind and infall, as well as the cloud rotation rate Ω0 and time since the start of infall. Breakout does occur for realistic parameter choices. The actual breakout times would change if we relaxed the assumption of perfect mixing between the wind and infall material. Our expanding shells do not exhibit the collimation of observed jets but continue to expand laterally. To halt this expansion, the density in the envelope must fall off less steeply than in our model.