  Observations of narrow radio-emitting filaments near the Galactic center have
been interpreted in previous studies as evidence of a pervasive vertical (i.e.
perpendicular to the Galactic plane) milliGauss magnetic field in the central
150 pc of the Galaxy. A simple cylindrically symmetric model for the
equilibrium in this central region is proposed in which horizontal (i.e.
parallel to the Galactic plane) magnetic fields embedded in an annular band of
partially ionized molecular material of radius 150 pc are wrapped around
vertical magnetic fields threading low-density hot plasma. The central vertical
magnetic field, which has a pressure that significantly exceeds the thermal
pressure of the medium, is confined by the weight of the molecular material.
The stability of this equilibrium is studied indirectly by analyzing a
uniformly rotating cylinder of infinite extent along the z axis in cylindrical
coordinates (r,theta,z), with low-density plasma and an axial magnetic field at
r< 150 pc, high-density plasma and an azimuthal field at r> 150 pc, and a
gravitational acceleration g* proportional to r directed in the negative-r-hat
direction. The density profile and gravity tend to destabilize the plasma, but
the plasma tends to be stabilized by rotation and magnetic tension--since the
interface between the high and low-density plasmas can not be perturbed without
bending either the horizontal or vertical field. It is shown analytically that
when beta= 8(pi)p/B^2 is small and the dense plasma is supported against
gravity primarily by rotation, the necessary and sufficient condition for
stability to k_z=0 modes is |g| < (2|Omega| a), where g = g* - Omega^2 r is the
effective gravity, Omega is the uniform angular velocity, and "a" is the sound
speed in the dense plasma.
