## 3. Kelvin-Helmholtz instabilities in superwinds of primeval galaxies: simulation resultsWhereas in the preceding section we described an analytic treatment
of the linear evolution of the KH mode in partially ionized plasmas,
in this section we show results of numerical simulations of the linear
and non-linear evolution of KH modes in the appropriate parameter
régime. These first self-consistent simulations of the full KH
dynamics in 2-fluid systems are carried out with an explicit
plasma-neutral gas fluid code (Birk & Otto 1996). As distinct from
analytical estimates for the linear evolution of the KH modes we do
not need to assume incompressibility, and we now include the balance
equations for the thermal pressures of both the ionized and the
neutral gas components ( where we assume the same adiabatic index for both fluid components. The integration scheme is based on the Leapfrog algorithm that is of second order in space and time and has the advantage of very low numerical diffusion. Spurious magnetic reconnection due to uncontrolled numerical diffusion can be avoided almost completely (cf. discussion by Frank et al. 1996 and Birk et al. 1999). The balance equations are integrated in a dimensionless form. They are normalized by a typical magnetic field strength , a typical mass density , a characteristic length scale , the Alfvén velocity , the Alfvénic transit time and the magnetic pressure . As in Sect. 3 we choose and kpc. The wind velocity is, as before, and the initial homogeneous magnetic field is chosen as G. This order of magnitude can be expected from the compressional amplification of seed fields during the protogalactic collapse (cf. Lesch & Chiba 1995). It should be noted that alternative simulation runs with a somewhat stronger initial magnetic field do not differ significantly from the results shown and discussed below as long as Kelvin-Helmholtz modes can be excited. In particular, the magnetic field amplification is comparable and happens on almost the same timescale. This is to be expected since the energy density of the initial magnetic field is much smaller than the kinetic energy of the wind plasma. In the present simulations we choose a small homogeneous background
resistivity in order to smooth gradients that otherwise could give
rise to numerical instabilities. For the effective collision frequency
we choose . The constant background
resistivity chosen corresponds to a magnetic Reynolds number of
. The effects of varying resistivity
have been discussed by Birk et al. (1999). A lower background
resistivity results in a slightly higher maximum magnetic field
strength. The calculations are performed in a mean velocity observer
frame. The wind proceeds in the For the simulations we use a 3-dimensional code with a start
configuration mentioned above. However, here, we only resolve the
2-dimensional dynamics. The simulation box is given by
, ,
and in units of 1kpc. The numerical
grid points are equidistant, and are chosen to be
. This means that we are not applying
strict invariance in the third dimension but do not resolve the
dynamics in the Fig. 3 illustrates the self-consistent evolution of the unstable KH
mode after 50 (left plot), 100 (middle plot) and 200 (right plot)
dynamical (Alfvénic transit) times, i.e. after 16Myr and 32Myr
and 80Myr, respectively. Here, and in the following plots we show cuts
at the -half plane. The arrows
indicate the flow in the
© European Southern Observatory (ESO) 2000 Online publication: December 8, 1999 |