X-rays in Cepheids: XMM-Newton Observations of $eta$ Aql

X-ray bursts have recently been discovered in the Cepheids $delta$ Cep and $beta$ Dor modulated by the pulsation cycle. We have obtained an observation of the Cepheid $eta$ Aql with the XMM-Newton satellite at the phase of maximum radius, the phase at which there is a burst of X-rays in $delta$ Cep. No X-rays were seen from the Cepheid $eta$ Aql at this phase, and the implications for Cepheid upper atmospheres are discussed. We have also used the combination of X-ray sources and Gaia and 2MASS data to search for a possible grouping around the young intermediate mass Cepheid. No indication of such a group was found.