Rayleigh-Taylor stability of a strong vertical magnetic field at the Galactic center confined by a disk threaded with horizontal magnetic field

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 similar to 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 similar to 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 -(r) over cap direction. Simple profiles are assumed for the density rho, pressure p, and field strength B, with the sound speed and Alfven speeds proportional tor within the dense plasma. 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 cannot be perturbed without bending either the horizontal or vertical field. Normal modes proportional to e(im theta + ikz z - i sigmat) with k(z) = 0 and m not equal 0 are studied. Such modes neither bend nor compress the axial field at r < 150 pc but allow compressions of the dense plasma along the azimuthal magnetic field that enhance the destabilizing role of gravity. It is shown analytically that when <beta> = 8 pip/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. Since the effective gravity is determined by the degree to which magnetic (and to a lesser degree pressure) forces support the dense plasma, the stability criterion gives an upper limit on the strength of the axial magnetic field, which is similar to1 mG for Galactic center parameters.