We wish to clarify whether strong magnetic fields can be effectively generated in typically low-mass dwarf galaxies and to assess the role of dwarf galaxies in the magnetization of the Universe. We performed a search for radio emission and magnetic fields in an unbiased sample of 12 Local Group (LG) irregular and dwarf irregular galaxies with the 100m Effelsberg telescope at 2.64 and 4.85GHz. Magnetic fields in LG dwarfs are three times weaker than in the normal spirals (<4.2+-1.8muG). The production of total magnetic fields appears to be regulated mainly by the star-formation surface density, with the power-law exponent of 0.30+-0.04, or by the gas surface density (with the exponent 0.47+-0.09). In addition, we find systematically stronger fields in objects of higher global star-formation rate. The dwarf galaxies follow a similar far-infrared relationship (with a slope of 0.91+-0.08) to that determined for high surface brightness spiral galaxies. The magnetic field strength in dwarf galaxies does not correlate with their maximum rotational velocity, indicating a small-scale rather than a large-scale dynamo process. If magnetization of the Universe by galactic outflows is coeval with its metal enrichment, we show that more massive objects (such as Lyman Break Galaxies) can efficiently magnetize the intergalactic medium with a magnetic field strength of about 0.8nG out to a distance of 160-530kpc at redshifts 5-3, respectively. Several times weaker fields and shorter magnetization distances are expected from primordial dwarf galaxies. We also predict that most star-forming local dwarfs might have magnetized their surroundings up to about 0.1muG within about 5kpc distance. Strong magnetic fields (>6muG) are observed only in dwarfs of extreme characteristics while typical LG dwarfs are unsuitable objects for the efficient supply of magnetic fields to the intergalactic medium.
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