Abstract
Objectives

We simulate the interstellar medium (ISM) by solving numerically the 3-dimensional non-ideal magnetohydrodynamic (MHD) set of equations. The model includes the stellar gravity field in the solar neighbourhood, a stratified gas density, shearing due to differential rotation, radiative cooling and uv-heating.

For comparison we use simulations of purely hydrodynamic properties and then run them with the inclusion of a small seed magnetic field. The primary source of turbulence and heat is provided by supernovae (SNe). We include type I and type 2 SNe, which are exploded at rates similar to the observed rate in the solar neighbourhood and with a reasonably realistic randomised distribution by position.

The aim of this project is to produce a physically motivated dynamical structure for the ISM, which saturates to a quasi-steady state of turbulence, from which the typical temperature and density filling factors and turbulent velocities and vorticity can be calculated with respect to anisotropy and height of the ISM.

It is of interest to investigate the relationship between these variables and the rate of SNe. In addition the factors which determine the outward vertical velocity flows towards the galactic halo are of interest to understanding whether this constitutes a galactic wind or fountain.

In consideration of the magnetic field we investigate how these factors combine to influence the galactic dynamo. The mean galactic field appears to owe its structure to the rotational shear of the galaxy, whilst the random components appear to be strongly driven by the twisting and stretching from the persistent violent SNe events. Measurement and comparison of the mean and random components and there dependence on the rate of shear and SNe rate and distribution are of interest to understanding this process.

Achievements

Within the ISM extreme variations within the density, temperature and velocity occur at close proximity. Combined with the violent shock fronts found in SNe remnants these properties are very challenging to model numerically, whilst retaining the essential physics effectively.

Before commencing the project, we had successfully modelled the essential properties described previously using type I SNe only and reaching simulation lengths of order 100-200 Myrs. As high temperatures or high velocities are generated by events in the simulation eventually the time step required to simulate accurately the processes becomes so small the simulation effectively stalls.

Our challenge with this project was to include the more numerous type II SNe and to extend the life span of the simulation to around a Gyr, whilst continuing to reproduce effectively and accurately a physically motivated galactic model. It can take 10-100 Myrs for turbulence to evolve to saturated steady state. To verify that results we obtain from our simulations are steady states and not numerical oscillations, we need to sustain these steady states over longer periods.

During the project we succeeded in solving many of the numerical challenges and have produced a simulation which exceeded 500Myrs and did not stall due to numerical difficulties, but because our budget for computing time has run out. This simulation included only hydrodynamics, although a similar run with magnetic field has also run over 100Myrs. In general it appears similar runs with magnetic field consistently can exceed those without, because the field appears to resist the propagation of excessive velocities or temperatures.

The simulations have produced results with interesting temperature and density filling factors and characteristic velocity patterns, which appear to be consistent with observations and current theory. To have a robust set of results, however, additional runs incorporating various alternative parameters and investigating the effect of higher resolution. We have already established that our current resolution of 5 parsecs cells is the minimum required to represent SNe expansion consistently, and this may yet need to be smaller to detect the dynamo properties consistently.