## 4. Parameters of the modelWe consider the dynamics of the disk by setting the radius of the innermost boundary cell to , and the radius of the outer boundary cell to . The group of parameters and in the right-hand side of the continuity Eqs. (6)-(8) govern the interchange processes between the components. Following Köppen et al. (1995) we choose the mean stellar lifetime Myr, or in our units . The mass fraction of the newly formed massive stars was set to 0.12. This value corresponds to a Salpeter-IMF ranging from 0.1 to 100 and a lower mass limit of massive stars of 10 . The fraction of mass ejected by massive stars back to the interstellar medium was taken to be 0.9. The parameter was set to 0.1. With this choice, the maximum star-formation rate in our model is 0.025, or if the initial mass of the gaseous disk is equal to 0.5 in our units. This value of the star-formation rate is close to the maximum star-formation rate obtained in chemo-dynamical models for the evolution of disk galaxies (Samland 1994). We have assumed that the gas component of the disk is mainly composed of mono-atomic hydrogen with a volume polytropic index . The polytropic constant for the collisionless stellar component and the remnants was set to 2.0. There are a few arguments in favor of this choice. Marochnik (1966) found that in a rigidly rotating disk the dynamics of perturbations can be described by introducing the polytropic equation of state with . This value is consistent with the empirical "square root law" found by Bottema (1993) in his studies of nearby spiral galaxies. He found, that the surface density distribution of stars, and their radial velocity dispersion are related as . It is easy to see, that such a "square root law" requires the value of the effective polytropic index to be . Kikuchi et al. (1997) made a detailed comparison of the linear stability properties of the exact collisionless models investigated by Vauterin & Dejonghe (1996) with the stability properties of this model studied in a fluid dynamical approach. They found a full qualitative agreement between these two approaches. Thus, a fluid dynamical approximation can be used for the analysis of the multi-component disks. The constant was set to be 0.04 resulting in a Toomre-stable disk (for details, see Sect. 6). The values and have been set to twice this value. This choice corresponds to a larger "sound" velocity of the stars, by this mimicking as well the dynamical heating of disk stars as the lack of dissipation in the stellar component. All parameters including those which are not discussed in this section are listed in the tables in the appendix. © European Southern Observatory (ESO) 1999 Online publication: June 30, 1999 |