Global magnetohydrodynamical simulations of accretion tori

Global time-dependent simulations provide a means to investigate time-depen dent dynamic evolution in accretion disks. This paper seeks to extend previ ous local simulations by beginning a systematic effort to develop fully glo bal three-dimensional simulations. The nonlinear development of the magneto rotational instability is investigated using a time-explicit finite differe nce code written in cylindrical coordinates. The equations of ideal magneto hydrodynamics are solved with the assumption of an adiabatic equation of st ate. Both a Newtonian potential and a pseudo-Newtonian potential are used. Two simplifications are also explored: a cylindrical gravitational potentia l (the "cylindrical disk") and axisymmetry. The results from those simulati ons are compared with fully three-dimensional global simulations. The globa l simulations begin with equilibrium pressure-supported accretion tori. Two different initial held geometries are investigated: poloidal fields that a re constant along initial equidensity surfaces and toroidal fields with a c onstant ratio of gas to magnetic pressure. In both cases the magnetorotatio nal instability rapidly develops and the torus becomes turbulent. The resul ting turbulence transports angular momentum, and the torus develops an angu lar momentum distribution that is near Keplerian. A comparison with axisymm etric simulations shows that in three dimensions the magnetorotational inst ability can act as a dynamo and regenerate poloidal field, thereby sustaini ng the turbulence. As previously observed in local simulations, the stress is dominated by the Maxwell component. The total stress in the interior of the disk is approximate to 0.1-0.2 times the thermal pressure. At late time the disks are characterized by relatively thick configurations, with rapid time dependence and tightly wrapped, low-ill spiral structures.