Star clusters larger than $sim 10^{3}$ $M_odot$ contain multiple hot stars that launch fast stellar winds. The integrated kinetic energy carried by these winds is comparable to that delivered by supernova explosions, suggesting that at early times winds could be an important form of feedback on the surrounding cold material from which the star cluster formed. However, the interaction of these winds with the surrounding clumpy, turbulent, cold gas is complex and poorly understood. Here we investigate this problem via an accounting exercise: we use empirically determined properties of four well-studied massive star clusters to determine where the energy injected by stellar winds ultimately ends up. We consider a range of kinetic energy loss channels, including radiative cooling, mechanical work on the cold interstellar medium, thermal conduction, heating of dust via collisions by the hot gas, and bulk advection of thermal energy by the hot gas. We show that, for at least some of the clusters, none of these channels can account for more than a small fraction of the injected energy. We suggest that turbulent mixing at the hot-cold interface or physical leakage of the hot gas from the HII region can efficiently remove the kinetic energy injected by the massive stars in young star clusters. Even for the clusters where we are able to account for all the injected kinetic energy, we show that our accounting sets strong constraints on the importance of stellar winds as a mechanism for feedback on the cold interstellar medium.
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