Magnetic collimation by accretion discs of quasars and stars

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Abstract
After an historical introduction on the relationships between quasars, accretion discs and jets, the paper concentrates on the problem of collimation. When the central upward magnetic flux from an accretion disc is twisted relative to the returning downward flux, the force-free field splays out at a semi-angle of 60° and all the flux reaches out to infinity after only half a turn. However, when the accretion disc itself lies within a medium with an ambient pressure the field cannot splay out in this way because too much work is needed to push the medium away. Whereas the field initially splays out, it ceases to do so when B2/8π balances the ambient pressure. Thereafter it assumes a vertical cylindrical geometry in which each additional twist of the field produces an equal increment in the height of the cylinder. After many twists the pitch of the field becomes no greater but the cylinder becomes very tall and thin. It is suggested that these structures are the collimators that lead to the remarkably narrow jets seen in quasars and radio galaxies, and associated with the accretion discs of young stars leading to Herbig-Haro objects, etc. Taken to the extreme, the jets are primarily these growing towers of twisted magnetic field together with the currents that they carry. A simple analytic model of such a cylindrical tower is built from force-free fields and it is shown to have the properties of a stabilized pinch. A modification demonstrates how dynamical expansion will affect the model.

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