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Abell 407 (A407) is a unique galaxy cluster hosting a central compact groupof nine galaxies (named as 'Zwicky's Nonet'; G1 - G9 in this work) within a 30kpc radius region. The cluster core also hosts a luminous radio active galacticnucleus (AGN), 4C 35.06 with helically twisted jets extending over 200 kpc.With a 44 ks Chandra observation of A407, we characterize the X-ray propertiesof its intracluster medium (ICM) and central galaxies. The mean X-raytemperature of A407 is 2.7 keV and the $M_{200}$ is $1.9 \times 10^{14}{M_{\odot}}$. We suggest that A407 has a weak cool core at $r < 60$ kpc scalesand at its very center, $< 1$-2 kpc radius, a small galaxy corona associatedwith the strong radio AGN. We also conclude that the AGN 4C 35.06 host galaxyis most likely G3. We suggest that the central group of galaxies is undergoinga `slow merge' procedure. The range of the merging time-scale is $0.3\sim2.3$Gyr and the stellar mass of the future brightest cluster galaxy (BCG) will be$7.4\times10^{11} M_{\odot}$. We find that the regions which overlap with theradio jets have higher temperature and metallicity. This is consistent with AGNfeedback activity. The central entropy is higher than that for other clusters,which may be due to the AGN feedback and/or merging activity. With all thesefacts, we suggest that A407 is a unique and rare system in the local universethat could help us to understand the formation of a massive BCG.

Chandra view of Abell 407: the central compact group of galaxies and the interaction between the radio AGN and the ICM