We have performed time-dependent numerical simulations of the interstellar medium ( ISM ) which account for galactic shear and magnetic fields , vertical gravity , and a radiative cooling function for atomic gas .
This allows us to study the magnetorotational instability ( MRI ) in cloudy , vertically-stratified disks .
As in previous unstratified models , we find that thermal instability interacts with MRI-driven turbulence and galactic shear to produce a network of cold , dense , filamentary clouds embedded in a warm diffuse ambient medium .
This structure strongly resembles the morphology of HI gas observed in the 21 cm line .
There is significant thermally-unstable gas , but the density and temperature distributions retain the twin peaks of the classical two-phase ISM .
Independent of the total gas surface density and vertical gravity levels adopted , the midplane ratios of thermal to magnetic pressure are \beta = 0.3 - 0.6 , when the mean vertical magnetic field is 0.26 \mu G .
We analyze the vertical distributions of density and various pressure terms , and address what supports the ISM vertically .
All models become differentially stratified by temperature ; only when the cold mass fraction is small does turbulent mixing maintain a large cold-medium scale height .
Turbulent velocities of the cold gas also increase as the cold mass fraction decreases , but are generally low ( \sim 1 - 3 { km s ^ { -1 } } ) near the midplane ; they increase to > 5 { km s ^ { -1 } } at high |z| .
Turbulent amplitudes are higher in the warm gas .
The central thermal pressure is similar for all models even though the total weight varies by a factor 7 for a range of imposed vertical gravity ; in higher gravity models the increased weight is supported by increased magnetic pressure gradients .
Approximate vertical equilibrium holds for all models .
Finally , we argue that in the outer parts of galactic disks , MRI is likely able to prevent the development of self-gravitating instabilities and hence suppress star formation , even if cold gas is present .