Observations of hot Jupiter type exoplanets suggest that their orbital period distribution depends on the metallicity of their host star. We investigate here whether the impact of the stellar metallicity on the evolution of the tidal dissipation inside the convective envelope of rotating stars and its resulting effect on the planetary migration might be a possible explanation for this observed statistical trend. We use a frequency-averaged tidal dissipation formalism coupled to an orbital evolution code and to rotating stellar evolution models to estimate the effect of a change of stellar metallicity on the evolution of close-in planets. We consider here two different stellar masses: 0.4 and 1.0 $M_{odot}$ evolving from the early pre-main sequence phase up to the red giant branch. We show that the metallicity of a star has a strong effect on the stellar parameters which in turn strongly influence the tidal dissipation in the convective region. While on the pre-main sequence the dissipation of a metal poor Sun-like star is higher than the dissipation of a metal rich Sun-like star, on the main sequence it is the opposite. However, for the $0.4~M_{odot}$ star, the dependence of the dissipation with metallicity is much less visible. Using an orbital evolution model, we show that changing the metallicity leads to different orbital evolutions (e.g., planets migrate farther out from an initially fast rotating metal rich star). By using this model, we qualitatively reproduced the observational trends of the population of hot Jupiters with the metallicity of their host stars. However, more steps are needed to improve our model to try to quantitatively fit our results to the observations. Namely, we need to improve the treatment of the rotation evolution in the orbital evolution model and ultimately we need to consistently couple of the orbital model to the stellar evolution model.
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