Astron. Astrophys. 333, 27-30 (1998)

3. The model

3.1. Differential rotation

We consider galaxies to be differentially rotating turbulent disks embedded in a plasma of given conductivity (Elstner et al. 1990). In the simplest case the "plasma" is vacuum and the conductivity therefore vanishes. The thickness of the galaxy, H, is 4 kpc, its radius, , is 7.5 kpc.

The differentially rotating gas is described by a Brandt-type law with n = 2 (Donner & Brandenburg 1990; Sofue 1996) and = 2 kpc,

Thus the velocity in the outer part of the galaxy doesn't exceed

We assume this velocity to have the same value ( 100 km s^-1) in all our models.

3.2. Nonaxisymmetry

In order to take into account the influence of the spiral arms in density and diffusivity the profiles used by Otmianowska-Mazur & Chiba (1995) are adopted,

varying between 1 and . The profile is used for the density ( with ) as well as for the turbulence intensity ( with )

is the angular pattern speed of the spiral and is set to 13 Gyr^-1 in all calculations. The density contrasts are fixed with . The pitch angle is taken as in the present paper.

3.3. Vertical stratification

For the density stratification we take the empirical H I distribution of Dickey & Lockmann (1990) as an ansatz for our simplified galaxy model: a combination of two Gaussians of central densities 0.395 and 0.107 cm^-3 and scale heights of 212 and 530 pc respectively, and an exponential with central density 0.064 cm^-3 and a scale height of 403 pc. Then we have added a further Gaussian with mid-plane density 0.3 cm^-3 and dispersion 70 pc to include the molecular gas layer (cf. Bloemen 1987), and an exponential with scale height 1.5 kpc and a mid-plane density of 0.025 cm^-3 representing the extended ionized gas (Reynolds 1989). For sake of simplicity we assume that profile being valid in all parts of the galaxy.

Based on the given density stratification we take a common simplification of the vertical momentum equation as a possibility to calculate the turbulence intensity:

The used potential is essentially due to a self-gravitating isothermal sheet of stars with constant thickness

Again for sake of simplicity all radial dependencies are neglected. We set = 21.5 km s^-1 being the vertical velocity dispersion of the old disk stars and = 0.6 kpc. For details see Fröhlich & Schultz (1996) and Elstner et al. (1996). The mid-plane turbulent velocity was assumed to be 10 km s^-1.

The resulting vertical profile of the turbulent velocity we used in all our models is shown in Fig. 1.

Fig. 1. The maximal turbulent velocity calculated from Eq. (16).

© European Southern Observatory (ESO) 1998

Online publication: April 15, 1998
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