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

Aims: High-resolution imaging in several photometric bands can provide color and astrometric information of the wide-orbit component of Cepheid stars. Such measurements are needed to understand the age and evolution of pulsating stars. In addition, binary Cepheids have the potential to provide direct and model-independent distances and masses. Methods: We used the NAOS-CONICA adaptive optics instrument (NACO) in the near-infrared to perform a deep search for wide components around the classical Cepheids, Y~Oph, FF~Aql, X~Sgr, W~Sgr, and $\eta$~Aql, within a field of view (FoV) of $1.7\mathrm{"}\times 1.7\mathrm{"}$ ($3.4"\times 3.4"$for$\eta$Aql)\mathrm{.}Results:Wewereabletoreachcontrast$\Delta H = 5$-8magand$\Delta K_$\mathrm{s}$ = 4$-7magintheradiusrange$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 $r>0.2\mathrm{"}$, we ruled out the presence of companions with a spectral type that is earlier than a B7V, A9V, A9V, A1V, and G5V star, respectively. For $0.1\mathrm{"}<r<0.2\mathrm{"}$, no companions earlier than O9V, B3V, B4V, B2V, and B2V star, respectively, are detected. A component is detected close to $\eta$~Aql at projected separation $\rho = 654.7 \pm 0.9$masandapositionangle$PA = 92.8 \pm 0.1^\circ$. We estimated its dereddened apparent magnitude to be $m_H^0=9.34\pm 0.04$ and derived a spectral type that ranges between an F1V and F6V star. Additional photometric and astrometric measurements are necessary to better constrain this star and check its physical association to the $\eta$~Aql system.