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Astron. Astrophys. 329, 895-905 (1998)

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3. Summary of the dynamical calculations

The velocity fields for the dynamo program are generated by the N-body simulation code described in Salo (1991) and Salo and Laurikainen (1993). In the current simulations the gravitational potential was determined on a 2-dimensional logarithmic polar grid, with 108 azimuthal and 144 radial cells. The stellar component consists of 200 000 self gravitating particles, initially distributed in an exponential disc. The gravitational softening parameter [FORMULA] was [FORMULA] of the scale length, taken to be 3 kpc, and the initial value for Toomre's [FORMULA] -parameter was 1.0. The gas component is modelled by 40 000 inelastically colliding test particles: in each impact the normal component of the relative velocity of the colliding particles is reversed, and multiplied by the coefficient of restitution, taken to be 0.2. The initial random velocities of the gas particles were 5% of the circular velocity. The analytical halo is represented by an isothermal sphere potential.

Two different models were used that differed only in their disc-halo mass relation. In the first (Model I) the disc mass fraction (measured within 4 exponential scale lengths = 12 kpc of the centre) was 68%. This means that the disc dominates the rotation curve and the initially axisymmetric simulation system develops a strong bar that gives rise to strongly noncircular velocities. This results in a high gas cloud collision frequency, which leads to inflow and eventually leaves `holes' in the gas distribution. This is undesirable from the point of view of dynamo calculations (see Sect. 4) but perhaps corresponds to the situation in many barred galaxies: the bar area is often relatively deficient in neutral hydrogen - see, for example, NGC 1365 (Lindblad et al. 1996), NGC 1300 (Lindblad & Kristen 1996) and NGC 1433 (Ryder et al. 1996). In addition to this inflow, the gas component forms inner and outer rings which are related to resonances (Schwarz 1981, Byrd et al. 1994), and are often observed in barred galaxies (Buta 1995).

In the second model (Model II) the disc mass fraction was reduced to 41% (again measured within 12 kpc). The amplitude and the shape of the rotation curve are very similar to those of the first model, but now the halo dominates the initial rotation curve through most of the disc region except near the middle of the disc. The effect of the bar on the overall dynamics is much smaller, and so the inflow of gas is not as strong as in model I. There is an inner gas ring but globally the spiral structure resembles a multiarmed galaxy. No outer gas ring is formed.

It is important to note that the magnetic induction is not directly affected by variations of the simulated gas density, but depends only on the gas velocity field, the streaming motions being determined by the strength of the bar. In Model I the gas motions are essentially non-circular, while in Model II the deviations from the circular motion are of the order of [FORMULA]. The latter figure is consistent with observed non-circular motions, whereas the former model is perhaps only applicable to the most extreme cases. In what follows we mostly concentrate on model I: however, for reasons discussed below we have effectively reduced the values of the non-circular velocities used in our computations (see Sect. 5).

Numerical simulations indicate that the pattern speed of the bar decreases due to angular momentum exchange between the bar and the outer galaxy (this was already noticed by Sellwood 1981). In our present models this decrease is not high, only 17% during the whole evolution of model I (excluding the initial bar formation period). Similarly, the amplitude and shape of the bar show only little evolution. However, if our halo, as well as the disc, consisted of self gravitating particles, this would provide an additional interaction mechanism, and the slow-down of bar would probably then be faster (Little and Carlberg 1991). Including this effect would require a three-dimensional simulation, and could also show other evolutionary phenomena that are not seen in the present simulations.

An snapshot of the dynamical models is given in Fig. 1, where the stellar and gas distributions in Model I are shown about 2 Gyr after the MHD simulation was started. The gas particle velocities are also shown (in a frame co-rotating with the bar), and the magnetic field vectors at the same time, from the simulation described in Sect. 5.1.

[FIGURE] Fig. 1. Snapshots from the 2D model I calculation at time 2.2 Gyr. In the upper row, the left and right hand panels give the density contours of the stellar density distribution and the gas particle positions, respectively. The lower left panel shows the gas velocity vectors in a coordinate system that co-rotates with the bar, and on the right the corresponding magnetic field vectors are shown. The dashed outer circle in each frame is drawn at a radius of 12 kpc, the outer boundary of the MHD calculation.

We have not tested how the details of the velocity field would change if different methods (Smoothed Particle Hydrodynamical or a fluid dynamical treatment) were used. However, as similar morphological features (resonance rings, shock regions) are typically obtained in simulations with various methods (compare for example Schwarz 1981, Friedli and Benz 1993, Lindblad et al. 1996), there is no reason to assume that the accompanying velocity fields would be drastically different. Also, taking into account our current poor knowledge of the behaviour of ISM, none of the three methods can be preferred over the other two (Sellwood and Wilkinson, 1993).

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© European Southern Observatory (ESO) 1998

Online publication: December 16, 1997