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Astron. Astrophys. 353, 108-116 (2000)

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4. Discussion

It seems very likely that dwarf galaxies were the most abundant early structures in the Universe, and that they constituted "building blocks" for the formation of large present day galaxies. Superwinds of these primeval starbursting galaxies contribute efficiently to the magnetization of the IGM. In this contribution we have shown that unstable KH modes result in the rapid regeneration of the magnetic fields that are expelled, and thus, can produce relatively strong field strengths in the immediately surrounding IGM during this early epoch of galaxy formation. In our analysis we treated one single instability process excited by a linear mode perturbation. However, steady stellar activity in the dwarf galaxies should drive continuous winds that have KH unstable boundary layers. This will result in a continuous injection of amplified magnetic flux into the surrounding IGM. In our simulation study we find an amplification factor of about 20 for the parameters chosen. However, our quantitative result can only be regarded as an example for the parameters given and the only 2-dimensionally resolved dynamics. In really 3-dimensional configurations the evolution of the modes may be somewhat different (cf. Jones et al. 1999 for the pure MHD case). It can be expected that additional twisting in the third dimension allows for even stronger magnetic field amplification. More extensive numerical studies (see also below) are desirable and planned.

One may argue further that KH dynamics could produce even stronger magnetic field amplification. The development of KH vortices, and the consequent twisting and curling of magnetic field lines occurs on progressively smaller spatial scales as a turbulent cascade. Simple flux conservation arguments (cf. Biermann & Schlüter 1951) can be adduced to show that this process will continue until the local magnetic field is given by [FORMULA] ([FORMULA], [FORMULA] and [FORMULA] are, respectively, the turbulent velocity, spatial dimension of the turbulence elements, and the macroscopic fluid velocity). For simplicity we have assumed Kolmogorov-type turbulence. Our choice of parameters leads to [FORMULA]G. The magnitude of the amplification factor obtained by the KH simulations, [FORMULA], suggests that further local turbulent magnetic field amplification can be effective down to spatial scales of [FORMULA]cm (where [FORMULA] is the initial magnetic field transported by the wind before the onset of the KH instability). Eventually, on very small spatial scales, redistribution by magnetic reconnection will become important. In this context a careful consideration of the electrical resistivity is necessary. It should be treated as a function of the current density, i.e. as a localized anomalous resistivity, rather than as a constant background value as chosen in our present study. The choice of the magnitude of such a resistivity is motivated by the relevant kind of violation of ideal Ohm's law, e.g. particle inertia or microturbulence, and will limit the amplification of the magnetic field as a real physical effect.

Also, the interaction of different vortices excited in neighbored resonant layers should be considered in order to get reliable quantitative results for the amplification factor of the magnetic field. Such an interaction is to be expected since there should be numerous KH resonant layers in the highly filamentary superwinds (cf. Reuter et al. 1992). The description of the whole scenario of magnetic field amplification and flux redistribution is beyond the scope of the present contribution. A self-consistent numerical 3D-analysis to elaborate on the discussed processes will be addressed in future work.

The KH instability discussed here can be regarded as a general and basic plasma process that occurs in complex, one- and multifluid shear flows. Our analysis of KH modes in partially ionized plasma régimes should also have applications to the dynamics of accretion disks in active galactic nuclei, X-ray binary systems, and in the disks around young stellar objects.

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© European Southern Observatory (ESO) 2000

Online publication: December 8, 1999
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