On the Possible Correlation Between the Orbital Periods of Extra-solar Planets and the Metallicity of the Host Stars

We investigate a possible correlation between the orbital periods $P$ of the extra-solar planet sample and the metallicity [Fe/H] of their parent stars. Close-in planets, on a few-days orbits, are more likely to be found around metal-rich stars. Simulations show that a weak correlation is present. This correlation becomes stronger when only sigle stars with one detected planet are considered. We discuss several potential sources of bias that might mimic the correlation, and find they can be ruled out, but not with high significance. If real, the absence of very short-period planets around the stellar sample with [Fe/H] $<0.0$ can be interpreted as evidence of a metallicity dependence of the migration rates of giant planets during formation in the protoplanetary disc. The observed $P-$[Fe/H] correlation can be falsified or confirmed by conducting spectroscopic or astrometric surveys of metal-poor stars ([Fe/H] $< -0.5$) in the field.