Extreme Ultraviolet Emission from Abell 4059

We present the results of a search for Extreme Ultraviolet emission in A4059, a cluster with an X-ray emitting cluster gas. Our analysis of Extreme Ultraviolet Explorer (EUVE) Deep Survey observations of this cluster shows that it is associated with diffuse EUV emission. Outside the central 2 arcmin radius the entire EUV emission detected is explained by the low energy tail of the X-ray emitting gas. Within the central 2 arcmin region of the cluster we find a deficit of EUV emission compared to that expected from the X-ray gas. This flux deficit is discussed in the context of the cluster's cooling flow. The results derived for A4059 are compared to EUVE results obtained for other clusters such as Coma, Virgo, A1795, and A2199. As part of the study we have carried out a detailed investigation of the stability of the EUVE Deep Survey detector background. Based on long integrations of blank sky over 27 months we disprove claims of substantial time dependent changes in the detector background by R. Lieu and coworkers. We also show, contrary to the claim of R. Lieu and coworkers, that the images obtained with the detector are independent of the pulse height threshold of the detector over a substantial range of threshold settings.