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Y~Ophiuchi (Y~Oph) is a classical Cepheid reported to be as dim as a Cepheidof about half its pulsation period, and exhibits a low radial velocity andlight-curves amplitude. Our objective is to conduct hydrodynamical pulsationmodeling of Y~Oph to derive its distance and provide physical insight to itslow amplitude and luminosity, constrained by an extensive set of observations.We first perform a linear analysis on a grid of models using hydrodynamicalpulsation code \texttt{MESA-RSP} in order to find the combinations of mass,metallicity, effective temperature and luminosity resulting in linearexcitation of pulsations with period of about 17$\,$days. Then, for the bestcombinations of stellar parameters, we perform non-linear computations toobtain the full-amplitude pulsations of these models. Last, we compare theresults to a complete set of observations along the pulsation cycle. We adjustsimultaneously the distance, the color excess and circumstellar envelope (CSE)model to fit the light curves and the angular diameter. We find that allpulsation models at high effective temperature are in remarkable agreement withthe observations along the pulsation cycle. This result suggests that the lowamplitude of Y~Oph can be explained by its location close to the blue edge ofthe instability strip. We also find that a pulsational mass of about7-8$\,\mathrm{M}_\odot$ is consistent with a non-canonical evolutionary modelwith moderate overshooting, PL relation and \textit{Gaia} parallax. However, amuch lower mass below 5$\,$M$_\odot$ is required to match Baade-Wesselink (BW)distance measurements from the literature. We show that the combination of theimpact of the CSE on the photometry together with a projection factor of about1.5 explains the discrepant distance and luminosity values obtained from BWmethods.

Pulsation modelling of the Cepheid Y Ophiuchi with RSP/MESA. Impact of  the circumstellar envelope and a high projection factor on Baade-Wesselink  method