The Coma cluster at LOFAR frequencies I: insights into particle acceleration mechanisms in the radio bridge

Radio synchrotron emission from the bridges of low-density gas connecting galaxy clusters and groups is a challenge for particle acceleration processes. In this work, we analyse the Coma radio bridge using new LOw Frequency ARray (LOFAR) observations at 144 MHz. LOFAR detects the bridge and its substructures with unprecedented sensitivity and resolution. We find that the radio emission peaks on the NGC 4839 group. Towards the halo, in front of the NGC 4839 group, the radio brightness decreases and streams of radio emission connect the NGC 4839 group to the radio relic. Using X-ray observations, we find that thermal and non-thermal plasma are moderately correlated with a sub-linear scaling. We use archival radio data at 326 MHz to constrain the spectral index in the bridge, and quantify the distribution of particles and magnetic field at different frequencies. We find that the spectrum is steeper than $-1.4 \pm 0.2$, and that the emission could be clumpier at 326 MHz than at 144 MHz. Using cosmological simulations and a simplified approach to compute particle acceleration, we derive under which conditions turbulent acceleration of mildly relativistic electrons could generate the radio emission in the bridge. Assuming that the initial energy ratio of the seed electrons is $3 \cdot 10^{-4}$ with respect to the thermal gas, we are able to reproduce the observed luminosity. Our results suggest that the seed electrons released by radiogalaxies in the bridge and the turbulence generated by the motion of gas and galaxies are essential to produce the radio emission.