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Context. Previous numerical studies have shown that in protostellar outflows, the outflowing gas mass per unit velocity, or mass-velocity distribution m(v), can be well described by a broken power law∝v^–γ. On the other hand, recent observations of a sample of outflows at various stages of evolution show that the CO intensity-velocity distribution, closely related to m(v), follows an exponential law ∝exp(-v/v₀).
Aims. In the present work, we revisit the physical origin of the mass-velocity relationship m(v) in jet-driven protostellar outflows. We investigate the respective contributions of the different regions of the outflow, from the swept-up ambient gas to the jet.
Methods. We performed 3D numerical simulations of a protostellar jet propagating into a molecular cloud using the hydrodynamical code Yguazu-a. The code takes into account the most abundant atomic and ionic species and was modified to include the H₂ gas heating and cooling.
Results. We find that by excluding the jet contribution, m(v) is satisfyingly fitted with a single exponential law, with v₀ well in the range of observational values. The jet contribution results in additional components in the mass-velocity relationship. This empirical mass-velocity relationship is found to be valid locally in the outflow. The exponent v₀ is almost constant in time and for a given level of mixing between the ambient medium and the jet material. In general, v₀ displays only a weak spatial dependence. A simple modeling of the L1157 outflow successfully reproduces the various components of the observed CO intensity-velocity relationship. Our simulations indicate that these components trace the outflow cavity of swept-up gas and the material entrained along the jet, respectively.
Conclusions. The CO intensity-velocity exponential law is naturally explained by the jet-driven outflow model. The entrained material plays an important role in shaping the mass-velocity profile.