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Astron. Astrophys. 331, 524-534 (1998)

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1. Introduction

To understand the evolution of galaxies one may attempt to match the observational data by models which describe the global processes - star-formation rate, gas infall, gas loss - with suitable formulations. By adjusting free parameters, quite good fits can be achieved. However, the number of these free parameters often is uncomfortably large. Moreover, this approach may not lead to a unique identification of the dominant physical process, as the persisting G dwarf-'problem' (Pagel & Patchett 1975) and the formation of radial abundance gradients (Götz & Köppen 1992) illustrate.

Our chemodynamical approach (Hensler 1987, Theis et al. 1992, Samland et al. 1997) tries to describe as precisely as possible the known physical processes present in the interstellar medium (ISM) and its interaction with the stars. These local processes are coupled with the global dynamics of the gaseous and stellar components, constituting a physical description of the evolution of a galaxy. Since it is unrealistic to include all processes in their full complexity, one has to define a sufficiently simple but accurate network of interactions in the ISM. Our prescription, based on the three-component ISM model of McKee & Ostriker (1977) and on the formulations of Habe et al. (1981) and Ikeuchi et al. (1984), has successfully been coupled with the global dynamics for models of elliptical (Theis et al. 1992) and disk galaxies (Samland et al. 1997).

Another important aspect is the degree of non-linearity of the network which determines the behaviour of the model. Since the dependences of the rate coefficients are not well known, some caution is necessary to avoid the appearance of complex behaviour solely due to the mathematical formulation. We cannot yet fully settle these questions, but what is needed is a more complete understanding of the behaviour of this type of model and an identification of the crucial processes.

In their chemodynamical models Theis et al. (1992) find that most often the star-formation rate varies slowly with time, but under certain conditions it undergoes strong nonlinear oscillations, involving the condensation and evaporation of the cool clouds embedded in the hot intercloud gas. The phases of slow variation are due to an equilibrium caused by the self-regulation of the star-formation rate (SFR) whose efficiency is reduced as the massive stars heat the gas by their ionizing continuum radiation. In a partial network with a single gas phase Köppen et al. (1995) show that this equilibrium results in a quadratic dependence of the SFR on gas density - independent of what was assumed for the stellar birth function. Under realistic conditions this is quickly reached, and it is unconditionally stable, quite insensitive to the rate coefficients used.

The present study extends the network of Köppen et al. (1995) to two gas components, clouds and intercloud gas, described in Sect. 2. We investigate its behaviour by numerical solution which allows the extraction of analytical conditions and relations. This permits the identification of the origin of the oscillations of the SFR (Sect. 3), and the formulation of a physically consistent description (Sect. 4) which leads to the identification of a second equilibrium, namely that between condensation and evaporation of the clouds. In Sect. 5 we extend the prescription to the more realistic one by Samland et al. (1997), having condensation and evaporation occurring simultaneously in a cloud population.

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© European Southern Observatory (ESO) 1998

Online publication: February 16, 1998