Stability of Magnetized Disks and Implications for Planet Formation
  This paper considers gravitational perturbations in geometrically thin disks
with rotation curves dominated by a central object, but with substantial
contributions from magnetic pressure and tension. The treatment is general, but
the application is to the circumstellar disks that arise during the
gravitational collapse phase of star formation. We find the dispersion relation
for spiral density waves in these generalized disks and derive the stability
criterion for axisymmetric $(m=0)$ disturbances (the analog of the Toomre
parameter $Q_T$) for any radial distribution of the mass-to-flux ratio
$\lambda$. The magnetic effects work in two opposing directions: on one hand,
magnetic tension and pressure stabilize the disk against gravitational collapse
and fragmentation; on the other hand, they also lower the rotation rate making
the disk more unstable. For disks around young stars the first effect generally
dominates, so that magnetic fields allow disks to be stable for higher surface
densities and larger total masses. These results indicate that magnetic fields
act to suppress the formation of giant planets through gravitational
instability. Finally, even if gravitational instability can form a secondary
body, it must lose an enormous amount of magnetic flux in order to become a
planet; this latter requirement represents an additional constraint for planet
formation via gravitational instability and places a lower limit on the
electrical resistivity.
