Radio multifrequency observations of galaxy clusters. The Abell 399$-$401 pair

Galaxy clusters are assembled via merging of smaller structures, in a process that generates shocks and turbulence in the intra cluster medium and produces radio diffuse emission in the form of halos and relics. The cluster pair A399-A401 represents a special case: both clusters host a radio halo. Recent Low Frequency Array (LOFAR) observations at 140 MHz revealed the presence of a radio bridge connecting the two clusters along with two relic candidates. These relics include one South of A399 and the other in between the two clusters, in proximity of a shock front detected in X-ray observations. In this paper we present observations of the A399-A401 cluster pair at 1.7, 1.4, 1.2 GHz and 346 MHz from the Westerbork Synthesis Radio Telescope (WSRT). We detect the radio halo in the A399 cluster at 346 MHz, extending up to $\sim 650$ kpc and with a $125 \pm 6$ mJy flux density. Its spectral index between 140 MHz and 346 MHz is $α= 1.75 \pm 0.14$. The two candidate relics are also seen at 346 MHz and we determine their spectral indices to be $α= 1.10 \pm 0.14$ and $α= 1.46 \pm 0.14$. The low surface brightness bridge connecting the two clusters is below the noise level at 346 MHz, therefore we constrain the bridge average spectral index to be steep, i.e. $α> 1.5$ at 95% confidence level. This result favours the scenario where dynamically-induced turbulence is a viable mechanism to reaccelerate a population of mildly relativistic particles and amplify magnetic fields on scales of a few Mpcs. Key words: galaxies: clusters: general - galaxies: clusters: individual: Abell 399 - radio continuum: general