The relation between the diffuse X-ray luminosity and the radio power of
  the central AGN in galaxy groups
  Our understanding of how AGN feedback operates in galaxy clusters has
improved in recent years owing to large efforts in multi-wavelength
observations and hydrodynamical simulations. However, it is much less clear how
feedback operates in galaxy groups, which have shallower gravitational
potentials. In this work, using very deep VLA and new MeerKAT observations from
the MIGHTEE survey, we compiled a sample of 247 X-ray selected galaxy groups
detected in the COSMOS field. We have studied the relation between the X-ray
emission of the intra-group medium and the 1.4 GHz radio emission of the
central radio galaxy. For comparison, we have also built a control sample of
142 galaxy clusters using ROSAT and NVSS data. We find that clusters and groups
follow the same correlation between X-ray and radio emission. Large radio
galaxies hosted in the centres of groups and merging clusters increase the
scatter of the distribution. Using statistical tests and Monte-Carlo
simulations, we show that the correlation is not dominated by biases or
selection effects. We also find that galaxy groups are more likely than
clusters to host large radio galaxies, perhaps owing to the lower ambient gas
density or a more efficient accretion mode. In these groups, radiative cooling
of the ICM could be less suppressed by AGN heating. We conclude that the
feedback processes that operate in galaxy clusters are also effective in
groups.
