Magnetic Helix Formation Driven by Keplerian Disk Rotation in an External Plasma Pressure: The Initial Expansion Stage

Abstract

We study the evolution of a magnetic arcade that is anchored to an accretion disk and is sheared by the di †erential 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 there is a fundamental di †erence between Ðeld lines that are a †ected by the plasma pressure and those that are not (i.e., force free). Force-free Ðelds, while being twisted by the di †erential rotation of the disk, expand outward at an angle of D60¡ away from the rotation axis, consistent with the previous studies. These force-free Ðeld lines, however, are enclosed by the outer Ðeld lines, which originate from small disk radii and come back to the disk at large radii. These outer Ðelds experience most of the twist, and they are also a †ected most by the external plasma pressure. At large cylindrical radial distances, magnetic pressure and plasma pressure are comparable so that any further radial expansion of magnetic Ðelds is prevented or slowed down greatly by this pressure. This hindrance to cylindrical radial expansion causes most of the added twist to be distributed on the ascending portion of the Ðeld lines, close to the rotation axis. Since these Ðeld lines are twisted most, the increasing ratio of the toroidal component to the B Õ poloidal component eventually results in the collimation of magnetic energy and Ñux around the B R,z rotation axis. We discuss the difficulty with adding a large number of twists within the limitations of the magnetostatic approximation.

Polarization and Structure of Relativistic Parsec-Scale AGN Jets

“…Choudhuri & Konigl 1986). Secondly, it is probable that jets are electromagnetically dominated on parsec scales (Lynden-Bell 1996Ustyugova et al 2000;Li et al 2001;Lovelace et al 2002;; see also Section 6), so that their structure is determined by relativistic force-free electrodynamics. In this work, we assume that the jets are strongly magnetized and are described by relativistic force-free electrodynamics.…”

Poynting Jets from Accretion Disks

“…Here, we consider further the theory of Poynting outflows (Li et al 2001). We assume that magnetic field loops thread a differentially rotating, highly conducting Keplerian accretion disk at some initial time t ¼ 0.…”

“…with D à @ 2 =@r 2 À ð1=rÞð@=@rÞ þ @ 2 =@z 2 ; which is the GS equation for É (see, e.g., Lovelace et al 1987;Li et al 2001). Ampère's law gives H dl x B ¼ ð4=cÞ R dS x J, so that rB ðr; zÞ ¼ HðÉÞ is ð2=cÞ times the current flowing through a circular area of radius r (with normalẑ z) labeled by Éðr; zÞ ¼ const.…”

“…The self-similar inflation of a force-free field threading a non-Keplerian disk without outer boundaries was studied by Lynden-Bell & Boily (1994), and their solution for small twists is analogous to our low-twist solutions. The expansion of a force-free field into finite-pressure external plasma has been studied by Lynden-Bell (1996) and Li et al (2001), and the poloidal field is found to fairly uniformly fill the coronal space.…”

“…Theoretical studies have developed models for Poynting outflows from accretion disks (Lovelace, Wang, & Sulkanen 1987;Colgate & Li 1998). The present work represents a continuation of the study by Li et al (2001), in which selfconsistent, axisymmetric, nonrelativistic solutions of the Grad-Shafranov (GS) equation are calculated inside given conducting boundaries. The solutions are self-consistent in the respect that the twist of each field line is that due to the differential rotation of a Keplerian disk.…”