Magnetic jets from swirling discs

A broad swathe of astrophysical phenomena, ranging from tubular planetary nebulae through Herbig-Haro objects, radio galaxy and quasar emissions to gamma-ray bursts and perhaps high-energy cosmic rays, may be driven by magnetically dominated jets emanating from accretion discs. We give a self-contained account of the analytic theory of non-relativistic magnetically dominated jets wound up by a swirling disc and making a magnetic cavity in a background medium of any prescribed pressure, p(z). We solve the time-dependent problem for any specified distribution of magnetic flux P(R, 0) emerging from the disc at z = 0, with any specified disc angular velocity Ω_d(R). The physics required to do this involves only the freezing of the lines of force to the conducting medium and the principle of minimum energy.

In a constant pressure environment, the magnetically dominated cavity is highly collimated and advances along the axis at a constant speed closely related to the maximum circular velocity of the accretion disc. Even within the cavity the field is strongly concentrated towards the axis. The twist in the jet field <B_φ>/<|B_z|> is close to and the width of the jet decreases upwards. By contrast, when the background pressure falls off with height with powers approaching z^-4, the head of the jet accelerates strongly and the twist of the jet is much smaller. The width increases to give an almost conical magnetic cavity with apex at the source. Such a regime may be responsible for some of the longest strongly collimated jets. When the background pressure falls off faster than z^-4, there are no quasi-static configurations of well-twisted fields and the pressure confinement is replaced by a dynamic effective pressure or a relativistic expansion. In the regimes with rapid acceleration, the outgoing and incoming fields linking the twist back to the source are almost anti-parallel so there is a possibility that magnetic reconnections may break up the jet into a series of magnetic `smoke-rings' travelling out along the axis.