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We examine the particle acceleration mechanism in the Mpc-scale bridgebetween Abell 399 and Abell 401 and assess in particular if the synchrotronemission originates from first-order or second-order Fermi re-acceleration. Weuse deep (~40 hours) LOw-Frequency ARray (LOFAR) observations from Abell 399and Abell 401 and apply improved direction-dependent calibration to producedeep radio images at three different resolutions at 144 MHz. With apoint-to-point analysis we find in the bridge trends between the radio emissionfrom our new maps and X-ray emission from an XMM Newton observation. Byanalyzing our observations and results, we argue that second-order Fermire-acceleration is currently the most favoured process to explain the emissionfrom the radio bridge, where past AGN activity may be responsible for thesupply of fossil plasma needed for in-situ re-acceleration. The radio halosfrom Abell 401 and Abell 399 are also consistent with a second-order Fermire-acceleration model.

A deep study of A399-401: An application for wide-field facet calibration