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The evolution of magnetic fields in galaxies is still an open problem inastrophysics. In nearby galaxies the far-infrared-radio correlation indicatesthe coupling between magnetic fields and star formation. The correlation arisesfrom the synchrotron emission of cosmic ray electrons traveling through theinterstellar magnetic fields. However, with an increase of the interstellarradiation field (ISRF), inverse Compton scattering becomes the dominant energyloss mechanism of cosmic ray electrons with a typical emission frequency in theX-ray regime. The ISRF depends on the one hand on the star formation rate andbecomes stronger in starburst galaxies, and on the other hand increases withredshift due to the evolution of the cosmic microwave background. With a modelfor the star formation rate of galaxies, the ISRF, and the cosmic ray spectrum,we can calculate the expected X-ray luminosity resulting from the inverseCompton emission. Except for galaxies with an active galactic nucleus the mainadditional contribution to the X-ray luminosity comes from X-ray binaries. Weestimate this contribution with an analytical model as well as with anobservational relation, and compare it to the pure inverse Compton luminosity.Using data from the Chandra Deep Field Survey and far-infrared observationsfrom ALMA we then determine upper limits for the cosmic ray energy. Assumingthat the magnetic energy in a galaxy is in equipartition with the energydensity of the cosmic rays, we obtain upper limits for the magnetic fieldstrength. Our results suggest that the mean magnetic energy of young galaxiesis similar to the one in local galaxies. This points toward an early generationof galactic magnetic fields, which is in agreement with current dynamoevolution models.

X-Ray Emission from Star-Forming Galaxies - Signatures of Cosmic Rays and Magnetic Fields