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.
