Dynamics of a Magnetic Flux Tube in Differentially Rotating Disks

Abstract

We carried out three-dimensional magnetohydrodynamic simulations of the dynamics of a magnetic flux tube in rotating disks. The effects of spatial variation of gravity and differential rotation were taken into account. We adopted a local shearing box model (Hawley, Gammie, & Balbus, 1995) to study the dynamical evolution of an isolated, initially azimuthal flux tube. In rigidly rotating disks, the flux tube is twisted due to the coupling of Parker instability and Coriolis force (Chou et al., 1998). In differentially rotating disks, the magnetic energy may increase because the differential rotation stretches the twisted flux tube. Furthermore, magnetorotational instability (Balbus & Hawley, 1991) also affects the dynamical evolution of the flux tube. Figure 1 shows the simulation box and the initial condition of the simulation. An isolated horizontal flux tube whose radius is r is embedded in the Keplerian disk. The magnetic field is assumed to be purely toroidal. The model parameters are r, plasma β = (P _gas/P _mag) at the center of the flux tube, and the height of the initial flux tube is h. We assume a periodic boundary in azimuthal direction and a sliding periodic boundary in radial direction. Figure 2 shows the time development of (B²/8πP ₀₎ and (—B _x B _y/4πP ₀), where the bracket means spatial average. Figure 3 shows the isosurface of magnetic field strength (white surface) and magnetic field lines (gray) for a model with r = 0.2H, β = 1, and h = 1.0H where H is the scale height. We found that, in differentially rotating disks, (1) an isolated flux tube is destructed and generates turbulence due to the increase of magnetorotational instability; (2) intense azimuthal magnetic fields are intermittently created; and (3) after the initial amplification of magnetic energy saturates, the magnetic energy approaches a quasi-steady value. Numerical computations were carried out on VPP300/16R at NAOJ