  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.
