ICM cooling, AGN feedback and BCG properties of galaxy groups-Five
  properties where groups differ from clusters
  Using Chandra data for a sample of 26 galaxy groups, we constrained the
central cooling times (CCTs) of the ICM and classified the groups as strong
cool-core (SCC), weak cool-core (WCC) and non-cool-core (NCC) based on their
CCTs. The total radio luminosity of the brightest cluster galaxy (BCG) was
obtained using radio catalog data and literature, which was compared to the CCT
to understand the link between gas cooling and radio output. We determined
K-band luminosities of the BCG with 2MASS data, and used it to constrain the
masses of the SMBH, which were then compared to the radio output. We also
tested for correlations between the BCG luminosity and the overall X-ray
luminosity and mass of the group.
  The observed cool-core/non-cool-core fractions for groups are comparable to
those of clusters. However, notable differences are seen. For clusters, all
SCCs have a central temperature drop, but for groups, this is not the case as
some SCCs have centrally rising temperature profiles. While for the cluster
sample, all SCC clusters have a central radio source as opposed to only 45% of
the NCCs, for the group sample, all NCC groups have a central radio source as
opposed to 77% of the SCC groups. For clusters, there are indications of an
anticorrelation trend between radio luminosity and CCT which is absent for the
groups. Indications of a trend of radio luminosity with black hole mass
observed in SCC clusters is absent for groups. The strong correlation observed
between the BCG luminosity and the cluster X-ray luminosity/cluster mass
weakens significantly for groups.
  We conclude that there are important differences between clusters and groups
within the ICM cooling/AGN feedback paradigm.
