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The global star formation rate in disk galaxies has traditionally been viewed as a slowly and monotonically varying function of time, or even constant. Often, the energy injection of high-mass stars (ionization, winds, supernovae) is argued to produce a self-regulating mechanism which clamps the star formation rate at a value that can only change on a secular timescale. Studies using one-zone models to simulate the time evolution of the large-scale interstellar medium have indicated that, besides self-regulation solutions, oscillating and runaway states are also possible when either time delays or nonlinear interactions between the stars and the ISM components are included. All these models lack spatial degrees of freedom. An important question is whether the self-regulation or oscillations found in these one-zone models persist on a global scale when spatial couplings are introduced.
We present a pair of two-dimensional model simulations of the large-scale ISM. In each model, newly formed stars pump energy back into the turbulence, but star formation occurs only when the turbulent energy density of the local gas decays below a critical value, assuming a particular cooling function. Also, a self-propagating star-formation mechanism is mediated through the turbulent field. The first model is a network of coupled ordinary differential equations (i.e. coupled one-zone models). The second is a probablistic cellular automaton. In each case the local and global temporal dynamics and the emergent spatial star-formation patterns are examined.
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