A model of quasars and their associated jets as phenomena of magnetic selfcompression is presented. Magnetic field self-compression, as observed in laboratory plasma focus devices, results in increases in energy density of more than 108 and in even larger increases in transferred power density. Our model, based on the scaling of these phenomena to astrophysical dimensions, avoids the problems of gravitationallyconfined approaches. It presents a mechanism by which the energy of a quasar is immediately derived from a volume nearly 106 times larger than the observed quasar radiating volume and is ultimately derived from the volume of an entire protogalactic plasma cloud. The model's predictions of quasar energy, radiated power, lifetime, dimensions, density and rotational velocity are in good agreement with observations. Part II of this paper extends the model to radio galaxies and briefly discusses the role of similar self-compression processes in the origin of filamentary super-clusters of galaxies.
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