The Magnetic Field of a Contracting Gas Cloud: I. Strict Flux-freezing

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Abstract
A gravitationally-bound, isothermal, spherical magnetic cloud is imagined formed by non-homologous, spherically-symmetric compression of a uniform medium permeated by a uniform magnetic field. The field structure is derived assuming strict flux-freezing, and the consequent magnetic forces computed. Within the cloud the results do not differ much from the pre-dictions of the virial theorem. Outside the cloud, magnetic pinching generates a strongly compressed equatorial zone, with the radial magnetic force locally much greater than the mean value as given by the virial theorem. However, spontaneous straightening of the external field-lines and flow of gas down the field into the zone rapidly bring the magnetic and gravitational forces into local balance. Relaxation of the field into a dipole-type structure which does not exert excessive pmching forces, and with the cloud field effectively detached from the background field, is impossible as long as the constraint of strict flux-freezing is imposed.

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