Context. Star-forming dwarf galaxies can be seen as the local proxies of the high-redshift building blocks of more massive galaxies according to the current paradigm of the hierarchical galaxy formation. They are low-mass objects, and therefore their rotation speed is very low. Several galaxies are observed to show quite strong magnetic fields. These cases of strong ordered magnetic fields seem to correlate with a high, but not extremely high, star formation rate. Aims. We investigate whether these magnetic fields could be generated by the cosmic-ray-driven dynamo. The environment of a dwarf galaxy is unfavourable for the large-scale dynamo action because of the very slow rotation that is required to create the regular component of the magnetic field. Methods. We built a 3D global model of a dwarf galaxy that consists of two gravitational components: the stars and the dark-matter halo described by the purely phenomenological profile proposed previously. We solved a system of magnetohydrodynamic equations that include an additional cosmic-ray component described by the fluid approximation. Results. We found that the cosmic-ray-driven dynamo can amplify the magnetic field with an exponential growth rate. The e-folding time is correlated with the initial rotation speed. The final mean value of the azimuthal flux for our models is on the order of few μG and the system reaches its equipartition level. The results indicate that the cosmic-ray-driven dynamo is a process that can explain the magnetic fields in dwarf galaxies.
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