The magnetic fields in M31, NGC 7331, NGC 2841, NGC 6946, and our galaxy

A time-independent model for the radial distributions of gas and magnetic field has been applied to the galaxies Milky Way, M31, NGC 7331, and NGC 2841, in order to explain the gaseous ring patterns in spiral galaxies, and to NGC 6946 to see if this model is valid for galaxies without a gaseous ring. The model takes the gas pressure as its input data and solves the MHD equations to calculate the magnetic field responsible for the gas distribution. This field has an azimuthal component only, and can be used to predict synchrotron radio emission. A discussion about the dependence of the synchrotron radiation profiles obtained upon the assumed relationN ₀(,B) for the cosmic-ray density per unit energy as a function of gas density and field strength, is here considered in detail. It is shown that a relation of the typeN ₀/B, which takes into account the loss of energy of the cosmic-relativistic electrons, yields good agreement with the observations.