The opening angles of some protostellar outflows appear too narrow to match the expected core–star mass efficiency (SFE) = 0.3–0.5, if the outflow cavity volume traces outflow mass, with a conical shape and a maximum opening angle near 90°. However, outflow cavities with a paraboloidal shape and wider angles are more consistent with observed estimates of the SFE. This paper presents a model of infall and outflow evolution based on these properties. The initial state is a truncated singular isothermal sphere which has mass ≈ 1 M _⊙ , freefall time ≈ 80 kyr, and small fractions of magnetic, rotational, and turbulent energy. The core collapses pressure free as its protostar and disk launch a paraboloidal wide-angle wind. The cavity walls expand radially and entrain envelope gas into the outflow. The model matches the SFE values when the outflow mass increases faster than the protostar mass by a factor 1–2, yielding protostar masses typical of the IMF. It matches the observed outflow angles if the outflow mass increases at nearly the same rate as the cavity volume. The predicted outflow angles are then typically ∼50° as they increase rapidly through the stage 0 duration of ∼40 kyr. They increase more slowly up to ∼110° during their stage I duration of ∼70 kyr. With these outflow rates and shapes, the model predictions appear consistent with observational estimates of the typical stellar masses, SFEs, stage durations, and outflow angles, with no need for external mechanisms of core dispersal.
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