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tokens: of protons that decay into pions, f sec 0.7 is the ratio of secondary and total cosmic ray e , m p and m e are the masses of protons and electrons, and c is the speed of light. The normalization of the proton injection spectrum Q p, 0 can be directly related to the supernova rate via where 0.1 is the fraction of the supernova energy E SN 10 51 erg that is converted into kinetic energy of cosmic rays (Dorfi 2000 ). The Lorentz factor p, 0 10 9 eV/( m p c 2 ) 1 marks the low-energy end of the cosmic ray proton spectrum. When travelling through the interstellar medium, cosmic rays lose energy continuously. The total number N e () of e can be described as where the energy losses are determined by the cooling time-scale e . At steady state, we find The different energy loss channels are: ionization (ion), bremsstrahlung (brems), inverse Compton scattering (IC), synchrotron emission (synch), and galactic outflows (wind). The individual time-scales can be summarized as and result in the total cooling time-scale Here, T 6.6510 25 cm 2 is the Thomson cross-section, u B B 2 /(8) is the energy density of the magnetic field B , u ISRF is the energy density of the interstellar radiation field (ISRF), n is a gas density, H is the galactic scaleheight, v wind the velocity of the galactic wind, and is the e Lorentz factor. 2.2 Synchrotron emission in a galactic magnetic field In the presence of a magnetic field, cosmic rays perform spiral motions and hence are constantly accelerated. A single electron with a Lorentz factor results in the spectral power where K 5/3 ( x ) is the modified Bessel function of second kind and (see e.g. the review by Blumenthal Gould 1970 ). To find the synchrotron emission L , synch produced from the full population of cosmic rays, one has to integrate over the cosmic ray distribution, i.e. The last integral over the pitch angle is roughly 8.9 for a cosmic ray spectrum with a slope of 2.2 and the lower limit of the integration is e, 0 10 7 eV/( m e c 2 ) 20. We note that the synchrotron luminosity L synch, is directly proportional to the supernova rate , which determines the total number of cosmic rays (see equation 3 ). As the supernova rate is correlated with the SFR, synchrotron emission can be used to estimate a galaxys SFR. 2.3 Freefree emission and absorption At low frequencies and high gas densities, the interstellar medium is optically thick and synchrotron emission, holding the information about the SFR, is absorbed. The optically thick regime is characterized by an optical depth ff larger than 1. The value of ff depends on the electron temperature T e , the emission measure EM , and the frequency : with The number density of the free electrons n e can be related to the gas density via the ionization degree f ion : n e f ion n . The filling factor f fill describes the clumping of the medium (Ehle Beck 1993 ; Berkhuijsen, Mitra Mueller 2006 ; Beck 2007 ). Hence, the critical frequency crit at which ff 1, determining