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Aims: High-resolution imaging in several photometric bands can provide colorand astrometric information of the wide-orbit component of Cepheid stars. Suchmeasurements are needed to understand the age and evolution of pulsating stars.In addition, binary Cepheids have the potential to provide direct andmodel-independent distances and masses. Methods: We used the NAOS-CONICAadaptive optics instrument (NACO) in the near-infrared to perform a deep searchfor wide components around the classical Cepheids, Y~Oph, FF~Aql, X~Sgr, W~Sgr,and $\eta$~Aql, within a field of view (FoV) of $1.7"\times 1.7"$ ($3.4"\times3.4"$ for $\eta$~Aql). Results: We were able to reach contrast $\Delta H =5$-8\,mag and $\Delta K_\mathrm{s} = 4$-7\,mag in the radius range $r > 0.2"$,which enabled us to constrain the presence of wide companions. For Y~Oph,FF~Aql, X~Sgr, W~Sgr, and $\eta$~Aql at $r > 0.2"$, we ruled out the presenceof companions with a spectral type that is earlier than a B7V, A9V, A9V, A1V,and G5V star, respectively. For $0.1"< r < 0.2"$, no companions earlier thanO9V, B3V, B4V, B2V, and B2V star, respectively, are detected. A component isdetected close to $\eta$~Aql at projected separation $\rho = 654.7 \pm0.9$\,mas and a position angle $PA = 92.8 \pm 0.1^\circ$. We estimated itsdereddened apparent magnitude to be $m_H^0 = 9.34 \pm 0.04$ and derived aspectral type that ranges between an F1V and F6V star. Additional photometricand astrometric measurements are necessary to better constrain this star andcheck its physical association to the $\eta$~Aql system.

Searching for visual companions of close Cepheids. VLT/NACO lucky imaging of Y~Oph, FF~Aql, X~Sgr, W~Sgr and $\eta$~Aql