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It is recently proposed that cosmic rays generate a seed magnetic field inthe early universe. In this paper, we propose another generation mechanism ofmagnetic fields by cosmic rays, which is the Biermann battery driven byresistive heating induced by the streaming of cosmic rays. This mechanism isdominant in small-scale, low-temperature, and strongly-ionized regions,compared with other previously proposed mechanisms. Because cosmic rays areexpected to be accelerated after the death of the first stars, this mechanismcan work during structure formation in the early universe. We show that itmakes the seed magnetic field with sufficient strength for the subsequentdynamo to amplify it to the micro Gauss level in the current galaxies.

Biermann Battery Powered by Resistive Heating Induced by Cosmic Ray Streaming