Poynting Jets from Accretion Disks

We give further considerations on the problem of the evolution of a coronal,force-free magnetic field which threads a differentially rotating, conductingKeplerian disk, extending the work of Li {\it et al.} (2001). This situation isdescribed by the force-free Grad-Shafranov (GS) equation for the flux function$\Psi(r,z)$ which labels the poloidal field lines (in cylindrical coordinates).The GS equation involves a function $H(\Psi)$ describing the distribution ofpoloidal current which is determined by the differential rotation or {\ittwist} of the disk which increases linearly with time. We numerically solve theGS equation in a sequence of volumes of increasing size corresponding to theexpansion of the outer perfectly conducting boundaries at ($R_{m}, Z_{m}$). Theouter boundaries model the influence of an external non-magnetized plasma. Thesequence of GS solutions provides a model for the dynamical evolution of themagnetic field in response to (1) the increasing twist of the disk and (2) thepressure of external plasma. We find solutions with {\it magneticallycollimated} Poynting jets where there is a {\it continuous} outflow of energy,angular momentum, and toroidal magnetic flux from the disk into the externalspace.Comment: 9 pages, 10 figure