At the highest level of resolution we have had the study of Balsara et al. (2004), Piontek and Ostriker (2007) and Mac Low et al. (2005) in 2003 pc3 domains. Too small to include large scale structure, such as density stratification or spiral arms, these studies were able to relate the relationship of turbulence from SN or MRI, with dynamo amplification.
They were able conclude that MRI could be a significant source of turbulence in the galaxy and in particular in the outer galaxy away from SN activity. The presence of cold dense filaments, they demonstrated, were not closely correlated to the dynamics of the SN remnants. Instead they appeared to be a product of generalised turbulence and gravitational instability.
Finally they found dynamo amplification rate was sensitive to the level SN rate up to an upper bound of between 12 & 40 × the solar neighbourhood rate. Amplification of the magnetic field was also increased by greater intermittency in the SN rate. Independent of SN rate the dynamo is quenched once the ISM is saturated by hot gas.
Losing resolution, but gaining structure Korpi et al. (1999), de Avillez and Breitschwerdt (2007), Slyz et al. (2005), Ryan Joung et al. (2009) and Gressel et al. (2008) constructed models incorporating the density stratification of the ISM near the plane of the galactic disc.
Unlike the smaller models, the ISM does not become saturated by SN activity. The stratified structure permits the disc to expand and relax as the SN rate fluctuates in time and spatial distribution. This relieves the quenching effect of turbulent saturation on the magnetic dynamo.
However results for the dynamo have been mixed. Korpi et al. (1999) and Gressel et al. (2008) did not find a dynamo with solar neighbourhood model parameters, and Gressel et al. (2008) only found the dynamo with differential rotation 2 and 4 × the galactic rate. Both these models used non-ideal MHD, where magnetic reconnection may dampen the dynamo in the critical cold dynamic filaments. The numerical values for resistivity are of course much higher than the realistic values observed in the ISM. de Avillez and Breitschwerdt (2007) did not investigate the dynamo but included a 5 µG magnetic field using ideal MHD within their later work.
With a vertical range of 20 kpc de Avillez and Breitschwerdt (2007) were able to include elements of the galactic fountain and without boundary mass losses, could sustain simulations over 400 Myr. They found that an excess of 200 Myr was required to completely saturate and establish an equilibrium state for the disc-halo cycle. They identified the scale height of the disc-halo interface at about ± 1.5 kpc. The additional height was required to allow the hot gas in the halo to cool and rain back to the disc.
Despite outflow boundary conditions, and hence mass losses over the duration of the simulation, Gressel et al. (2008) were able to sustain their simulations over 1 Gyr. Once the turbulent state had evolved they found the boundary flows were minimal, so much of the dynamical cycle could be contained within a domain height of ± 2 kpc.
On the grand scale Hanasz et al. (2009) were able to produce a familiar model of the spiral structure of the galaxy. Restricted to isothermal models, they found the structure of the spirals sensitive to the CR diffusion. In addition the 2D study of Slyz et al. (2005) found the structure was also dependent on the temperature of the ISM, as parameterized by sound speed.
These models have informed our understanding of how the ISM behaves on different scales across a range of parameters. It is also clear that the interaction of temperature, density, magnetic field and cosmic rays combined are significantly altered in the absence of any one of these with unexpected consequences.
The challenge is to successfully incorporate all these elements over a number of physically meaningful scales. Global models of galaxies are indispensable, with sufficiently high resolution to include the small-scale physics. To resolve SNe remnants requires a resolution under 53 pc3. For the random field dynamo we may require scales < 23 pc3. The gravitational field (and self-gravitation of the gas) needs to be included, the latter requiring scales below 1pc. Density waves are expected to interact with the magnetic fields and need to be considered. Arm and inter-arm modelling would require domains extending a few kpc in the galactic plane. To include even the lowest reach of the halo, would require a vertical range of at least 4 kpc.