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Astron. Astrophys. 328, 121-129 (1997)

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7. Stratified distribution of the interstellar medium

The distribution of the interstellar medium in the z direction perpendicular to the galactic plane is approximated with one or more Gaussian and exponential components (Dickey & Lockman, 1990). Here, we examine the expansion of bubbles in a medium with [FORMULA] stratification and discuss how the shell fragmentation is influenced.

For simplicity, we start with one Gaussian component

[EQUATION]

where [FORMULA] is the gaussian half-thickness of the disk. Later, the discussion will be extended also to multi-component disks.

The results of computer simulations are presented in Fig. 4, where the radius of the shell in the galactic plane r, the maximum distance of the shell to the galactic plane z and the maximum value of the fragmentation integral [FORMULA], are given as functions of time for different values of [FORMULA].

[FIGURE] Fig. 4. Radius r (a), vertical extension z (b) and the fragmentation integral [FORMULA] (c) as a function of time, and the shape of the shells after 20 Myr of expansion (d) for different values of [FORMULA]. Solid line: [FORMULA] pc, long dash line: [FORMULA] pc, short dash line [FORMULA] pc.

The time sequence of snapshots for the case of the thick disks, with [FORMULA] pc is shown in Fig. 5. The evolution is similar to the case of a homogeneous medium. Due to the density gradient perpendicular to the plane the shell is slightly stretched in the z -direction, which is shown with larger values of z in relation to r for given time. The instability belt, where the fragmentation conditions (3) and (7) are fulfilled grows with time, and before the time [FORMULA] in the most unstable parts near the galactic plane is reached, almost all the shell becomes unstable.

[FIGURE] Fig. 5. The time sequences of shell expansion in the one component thick gaussian disk with [FORMULA] = 500 pc. The snapshots are for t = 10, 20, 30, 40 and 50 Myr. A black color shows regions where the value of fragmentation integral [FORMULA] = 0, a white color shows regions where the value [FORMULA]. The black line has a length of 1 kpc.

In disks of medium thickness, [FORMULA] pc, the shells are rather elongated reaching [FORMULA] kpc, and the instability belt is restricted to [FORMULA] pc only. Parts of the shell at larger heights are always gravitationally stable.

In thin disks, [FORMULA] pc the bubble blows out to [FORMULA] 3 - 4 kpc. It is always stable, even near to the galactic plane. There the instability conditions are fulfilled at some time, however the shell decelerates to the speed of sound well before [FORMULA] and the fragments reexpand (see Fig. 4).

For a comparison, a multi-component disk as proposed for the solar vicinity in the Milky Way by Dickey & Lockman (1990) was tested. The z distribution of interstellar medium is given as

[EQUATION]

where [FORMULA] = 212 pc, [FORMULA] = 530 pc and [FORMULA] = 403 pc. This multi-component disk is compared to a disk with only one gaussian or one exponential component of the scale-heights 200 pc. All the three disks have the same surface density [FORMULA]. The results of simulations are shown in Fig. 6. In the multi-component disk the shells reach smaller distances from the galactic plane than in disks with one gaussian or exponential component, and the fragmentation integrals evolve with time in a similar way as in the case of the disk with one gaussian component.

[FIGURE] Fig. 6. The value of r, z and [FORMULA] are given as functions of time. Solid line: multi-component disk; long dash line: one component exponential disk; short dash line: one component gaussian disk.
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© European Southern Observatory (ESO) 1997

Online publication: March 24, 1998

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