Poynting jets from accretion disks

We give further consideration to the problem of the evolution of a coronal, force-free magnetic field that threads a differentially rotating, conducting Keplerian disk, extending the recent work of Li and coworkers. This situation is described by the force-free Grad-Shafranov (GS) equation for the flux function Psi(r, z) that labels the poloidal field lines ( in cylindrical coordinates). The GS equation involves a function H (Psi) describing the distribution of the poloidal current, which is determined by the differential rotation or twist of the disk that increases linearly with time. We numerically solve the GS equation in a sequence of volumes of increasing size corresponding to the expansion of the outer perfectly conducting boundaries at (R-m, Z(m)). The outer boundaries model the influence of an external nonmagnetized plasma. The sequence of GS solutions provides a model for the dynamical evolution of the magnetic field in response to ( 1) the increasing twist of the disk and (2) the pressure of external plasma. We find solutions with magnetically collimated Poynting jets in which there is a continuous outflow of energy, angular momentum, and toroidal magnetic flux from the disk into the external space. This behavior contradicts the commonly accepted theorem of solar plasma physics that the motion of the footpoints of a magnetic loop structure leads to a stationary magnetic field configuration with zero power, angular momentum, and flux outflows. In addition, we discuss magnetohydrodynamic simulations that show quasi-stationary collimated Poynting jets similar to our GS solutions. In contrast with the GS solutions, the simulations show a steady uncollimated hydromagnetic (nonforce-free) outflow from the outer part of the disk. The Poynting jets are of interest for the understanding of the jets from active galactic nuclei, microquasars, and possibly gamma-ray burst sources.