Vertical structure of a supernova-driven turbulent magnetized ISM

Stellar feedback drives the circulation of matter from the disk to the halo of galaxies. We perform three-dimensional magnetohydrodynamic simulations of a vertical column of the interstellar medium with initial conditions typical of the solar circle in which supernovae drive turbulence and determine the vertical stratification of the medium. The simulations were run using a stable, positivity-preserving scheme for ideal MHD implemented in the FLASH code. We find that the majority (\approx 90 %) of the mass is contained in thermally-stable temperature regimes of cold molecular and atomic gas at T < 200 K or warm atomic and ionized gas at 5000 K < T < 10^{4.2} K, with strong peaks in probability distribution functions of temperature in both the cold and warm regimes. The 200 - 10^{4.2} K gas fills 50-60 % of the volume near the plane, with hotter gas associated with supernova remnants (30-40 %) and cold clouds (< 10 %) embedded within. At |z| ~ 1-2 kpc, transition-temperature (10^5 K) gas accounts for most of the mass and volume, while hot gas dominates at |z| > 3 kpc. The magnetic field in our models has no significant impact on the scale heights of gas in each temperature regime; the magnetic tension force is approximately equal to and opposite the magnetic pressure, so the addition of the field does not significantly affect the vertical support of the gas. The addition of a magnetic field does reduce the fraction of gas in the cold (< 200 K) regime with a corresponding increase in the fraction of warm (~ 10^4 K) gas. However, our models lack rotational shear and thus have no large-scale dynamo, which reduces the role of the field in the models compared to reality. The supernovae drive oscillations in the vertical distribution of halo gas, with the period of the oscillations ranging from ~ 30 Myr in the T < 200 K gas to ~ 100 Myr in the 10^6 K gas, in line with predictions by Walters & Cox.