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When there are accretion discs jets of particles or radiations will be emitted in the direction parallel to the rotational axis.

My beginner level astronomy textbook just says that it is due to magnetic field but does not explain why.

So can anyone explain the mechanism in layman's terms? Thanks in advance!

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If you don't mind a layman's explanation, the first thing to understand is why the accretion disk is flat and that's a product of conservation of angular momentum, explained very well in this video.

If we begin with a flat, rapidly rotating (or orbiting) disk of very hot matter, too hot for electrons to stay bound to atoms, so it's both hot and electrically charged, you get gonzo magnetic fields, which (by a process I don't understand well) creates magnetic field files that extends in twists both above and below the disc, see pretty pictures:

enter image description here

enter image description here

So, as the matter from the disk tries to fall inside the black hole, if there's too much matter, it can't all squeeze inside at once because mostly, black holes are quite tiny and the pressure and magnetism shoots a lot of the matter back out, primarily through the middle of the magnetic field lines.

That's a kind of simple explanation anyway. Correction is welcome.

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