On the nature of EXO 0423.4−0840

We present a Chandra observation of the candidate BL Lac object EXO 0423.4?0840. The X-ray emission from EXO 0423.4?0840 is clearly extended, and is associated with an optical early-type galaxy, MCG-01-12-005, at the centre of cluster ClG 0422-09. We do not detect a point source that can be associated with a BL Lac, but we found a small radio source in the centre of MCG-01-12-005. The cluster gas temperature mapped by the Chandra observation drops continuously from 80 kpc towards the centre, and is locally single phase. We measure a metallicity profile that declines outwards with a value  0.8 Z_⊙  in the centre, dropping to  0.35 Z_⊙  at larger radius, which we interpret as a superposition of cluster gas and a dense interstellar medium (ISM) in the central galaxy. Although the temperature profile suggests that conduction is not efficient, the ISM and intra-cluster medium seem not to have mixed. The entropy profile declines continuously towards the centre, in agreement with recent results on groups and clusters. The radio source appears to have had some effect in terms of gas heating, as seen in the small-scale (～10 kpc) entropy core, and the asymmetric hard emission on the same scale.