Relation between metallicities and spectral energy distributions of Herbig Ae/Be stars. A potential link with planet formation

(Abridged) The stellar metallicity, [M/H], may have important implications for planet formation. In particular, Kama et al. proposed that the deficit of refractory elements in the surfaces of some Herbig Ae/Be stars (HAeBes) may be linked to the presence of disk cavities likely caused by Jovian planets that trap the metal-rich content. This work aims to provide a robust test on the previous proposal by analyzing the largest sample of HAeBes with homogeneously derived [M/H] values, stellar, and circumstellar properties. [M/H] values of 67 HAeBes were derived based on observed spectra and Kurucz synthetic models. Statistical analyses were carried out aiming to test the potential relation between [M/H] and the group I sources from the spectral energy distribution (SED) classification by Meeus et al., associated to the presence of cavities potentially carved by giant planets. Our study robustly confirms that group I sources tend to have a lower [M/H] than that of group II HAeBes. A similar analysis involving SED-based transitional disks does not reveal such a relation, indicating that not all processes capable of creating dust holes have an effect on the stellar abundances. We also show that the observed [M/H] differences are not driven by environmental effects. Finally, group I sources tend to have stronger (sub-) mm continuum emission presumably related to the presence of giant planets. Indeed, literature results indicate that disk substructures probably associated to their presence are up to ten times more frequent in group I HAeBes. We provide indirect evidences suggesting that giant planets are more frequent around group I/low [M/H] stars than around the rest of the HAeBes. However, the direct test requires multiple detections of forming planets in their disks, so far limited to the candidate around the metal depleted ([M/H] = -0.35 +- 0.25) group I HAeBe star AB Aur.