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Summary A theory is proposed for the correlation between radio continuum (RC) and thermal far-infrared (FIR) radiation for normal spiral galaxies. In this theory, we assume global energy outputs of the FIR and cosmic rays to be proportional to the star formation rate, and adopt energy equipartition between cosmic rays and the interstellar magnetic field so as to keep dynamical stability and steady star formation in the galaxies. It is shown that the tight correlation between the RC and FIR emission results from a steady star formation process in the galaxies rather than both of them being simply from the same source. An important feature of the model is that, in the majority of galaxies, most of the cosmic ray electrons responsible for the radio emission at the observed frequencies escape. An approximate solution to the problem of electron propagation with a free escape boundary condition is derived and the emissivity of synchrotron radio emission is calculated. Direct evidence for the theory is the prediction of a non-unity slope for the correlation between RC and FIR, and this is observed. From small and less luminous galaxies to large and more luminous ones, we predict that there is a turning point above which most of the electrons will be trapped in the galaxies rather than escaping, and correspondingly the slope of the correlation will become unity. From a sample of data, we find this trend.

Implications of the correlation between radio and far-infrared emission for spiral galaxies