Magnetic helix formation driven by Keplerian disk rotation in an external plasma pressure: The initial expansion stage

We study the evolution of a magnetic arcade that is anchored to an accretio n disk and is sheared by the differential rotation of a Keplerian disk. By including an extremely low external plasma pressure at large distances, we obtain a sequence of axisymmetric magnetostatic equilibria and show that th ere is a fundamental difference between field lines that are affected by th e plasma pressure and those that are not (i.e., force free). Force-free fie lds, while being twisted by the differential rotation of the disk, expand o utward at an angle of similar to 60 degrees away from the rotation axis, co nsistent with the previous studies. These force-free field lines, however, are enclosed by the outer field lines, which originate from small disk radi i and come back to the disk at large radii. These outer fields experience m ost of the twist, and they are also affected most by the external plasma pr essure. At large cylindrical radial distances, magnetic pressure and plasma pressure are comparable so that any further radial expansion of magnetic f ields is prevented or slowed down greatly by this pressure. This hindrance to cylindrical radial expansion causes most of the added twist to be distri buted on the ascending portion of the field lines, close to the rotation ax is. Since these field lines are twisted most, the increasing ratio of the t oroidal B-phi component to the poloidal component B-R,B-z eventually result s in the collimation of magnetic energy and flux around the rotation axis. We discuss the difficulty with adding a large number of twists within the l imitations of the magnetostatic approximation.