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

Context. Most studies devoted to Herbig Ae/Be stars (HAeBes) assume solar metallicity. However, the stellar metallicity, [M/H], is a fundamental parameter that can strongly differ depending on the source and may have important implications for planet formation. It has been proposed that the deficit of refractory elements observed in the surfaces of some HAeBes may be linked to the presence of cavities in their disks and is likely caused by Jovian planets that trap the metal-rich content. Aims. This work aims to provide a robust test on the previous proposal by analyzing the largest sample of HAeBes characterized by homogeneously derived [M/H] values and stellar and circumstellar properties. Methods. The spectra of 67 HAeBes, along with their well-known properties drawn from our previous work, have been collected from the ESO Science Archive Facility. Their [M/H] values were derived based on the comparison with Kurucz synthetic models. Statistical analyses were carried out with the aim to test the potential relation between [M/H] and the Meeus group I sources, with spectral energy distributions (SEDs) associated with the presence of cavities potentially carved by giant planets. We critically analyzed the eventual link between [M/H], the SED groups, and the presence of such planets. Results. Our statistical study robustly confirms that group I sources tend to have a lower [M/H] (typically similar to -0.10) than that of group II HAeBes (similar to +0.14). A similar analysis involving SED-based transitional disks, with infrared excess only at wavelengths of >= 2.2 mu m, does not reveal such a relation with [M/H]. This result indicates that not all processes capable of creating holes in the inner dust disks end up having an effect on the stellar abundances. The spatial distributions of group I and II sources are similar, at least within the available range of distances to the galactic centre and the galactic plane, for which the observed [M/H] differences are not driven by environmental effects. In addition, 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 with the presence of giant planets are up to ten times more frequent in group I HAeBes than in group II. Finally, along with the metallicities derived for the whole sample, surface gravities and projected rotational velocities are additional outcomes reported in this work. Conclusions. We provide indirect evidence to suggest that giant planets are more frequent around group I/low [M/H] stars than around the rest of the HAeBes. However, a direct test of the previous hypothesis requires multiple detections of forming planets in their disks. Such detections have so far been limited to the candidate around the metal depleted ([M/H] = -0.35 +/- -0.25) group I HAeBe star AB Aur, which is consistent with our findings.