Periodic bursts of star formation are a desired feature in any model of the evolution of a gas-star system at relatively small scales. In the present study we show that star formation bursts appear naturally as a consequence of the delayed action of a particular self-regulated process of star formation, even when the stationary dynamical equilibrium is stable in the absence of the delay. In order to show the effect of the delay, we consider a one-zone model that schematically takes into account various relevant processes for the mass exchange between stars, clouds, warm gas, and hot gas. The model discriminates between massive stars, obscured massive stars, long-lived stars, and stellar remnants and also considers gas accretion. The delayed self-regulation produces an overstability that drives strong oscillations around the self-regulated state in all the variables. The delay is explicitly associated to the time that massive stars spend obscured in the parent cloud after their formation and implicitly associated to the time between the condensation of the warm gas and the appearance of nonobscured massive stars. For a different self-regulated model of the evolution of interstellar clouds and star formation, Struck-Marcel & Scalo obtained similar conclusions. These results suggest that strong oscillations in the local star formation rate should appear whenever a long enough delay is associated to a regulating mechanism of star formation.
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