## 5. Numerical resultsWe computed the non-vanishing components of the alpha- and
diffusivity tensors (Eqs. (24) and (25)) at 15 equidistant
Galactic radii ranging from 5 to 12 kpc. Inside 5 kpc, our
model for the interstellar gas distribution becomes too uncertain and
is no longer approximately plane-parallel. Beyond 12 kpc, the
dynamo parameters have dropped to less than one hundredth of their
maximum value. In Fig. 8, we display the results of the
computation at
It clearly appears that the contribution from isolated SNs (thin
line, visible only for ) is everywhere
negligible compared to that from SBs (thick line): isolated SNs give
rise to less than 0.1% of the alpha-parameters and to less than 1% of
the escape velocity and of the magnetic diffusivities. At first sight,
this huge difference is somewhat surprising, given that isolated and
clustered SNs have roughly the same Galactic frequency (see below
Eq. (20)). However, as mentioned in Paper III, when The curves relative to are similar in shape to those obtained in Paper III, but the overall magnitudes and characteristic scale heights are both smaller, mainly because a higher interstellar pressure was adopted in the present study. The If all SBs were cylindrical and merged in one go (i.e.,
and independent of
The behavior of the vertical alpha-parameter is a little more
subtle. As explained in Paper III, the sign of
is closely related to the shape of SBs. Consider, for instance, the SB
displayed in Fig. 10, and suppose that the mean magnetic field,
, is uniform and oriented in the positive
We now turn to the On the other hand, there exist a few particularly luminous
off-center SBs (like SB 4 in Fig. 9b) which are so severely
affected by the gas density stratification that they actually grow
higher at smaller radii. After bursting through the dense gas layer,
these SBs find it easier to expand upward at smaller To close up this section, we provide contour plots of the dynamo parameters in Fig. 11. Because of the limited radial range of our computation, we had to extrapolate the numerical results presented above. Inside kpc, we opted to take the functions obtained at 5 kpc and simply weight them by the factor , where is the SB rate per unit area (Fig. 6b) and the exponential factor is meant to account for the increase in interstellar pressure toward the Galactic center. Outside kpc, all functions have become so small that the exact extrapolation procedure has no impact on the contour plots.
Broadly speaking, the dynamo parameters peak at
kpc and (except for
) kpc. The fact
that the peak in dynamo activity occurs farther out than the peak in
SB rate (see Fig. 6b) is a direct consequence of the longer
lifetime and larger volume reached by SBs at greater The standard Galactic dynamo operates through a combination between the large-scale differential rotation and the alpha-effect. The strength of these two processes against magnetic diffusion can be measured by the dimensionless numbers and respectively, and their combined strength is given by the dynamo number, With , , and (appropriate for a disk geometry), the dynamo number works out to be in the peak region. This is a comfortable value, large enough to guarantee dynamo action (when ) and small enough to exclude very high dynamo modes. When , dynamo action also requires that the ratio be less than a critical value (Schultz, Elstner, & Rüdiger 1994); this condition, too, is fulfilled in the peak region, where we find . Two more conclusions can be drawn from the values of the ratio
in the peak region. First, for
, this ratio yields the magnetic pitch angle,
© European Southern Observatory (ESO) 1998 Online publication: June 18, 1998 |