SHOTGLAS: I. The ultimate spectroscopic census of extreme horizontal branch stars in ω Centauri⋆⋆⋆

The presence of extreme horizontal branch (EHB) and blue hook stars in some Galactic globular clusters (GGCs) constitutes one of the remaining mysteries of stellar evolution. In this paper, we focus on $\omega$ Cen, a peculiar, massive GGC that hosts multiple stellar populations. We use non-LTE model atmospheres to derive atmospheric parameters (Teff, log g and N(He)/N(H)) and spectroscopic masses for 152 EHB stars in the cluster. This constitutes the largest spectroscopic sample of EHB stars ever analyzed in a GGC and represents ~20% of the EHB population of $\omega$ Cen. We also search for close binaries among these stars based on radial velocity variations. Our results show that the EHB population of $\omega$ Cen is divided into three spectroscopic groups that are very distinct in the Teff - helium abundance plane. The majority of our sample consists of sdOB stars that have roughly solar or super-solar atmospheric helium abundances. It is these objects that constitute the blue hook at $V >$ 18.5 mag in the $\omega$ Cen color-magnitude diagram. Interestingly, the helium-enriched sdOBs do not have a significant counterpart population in the Galactic field. Another major difference between the EHB stars in $\omega$ Cen and the field is the fraction of close binaries. From our radial velocity survey we identify two binary candidates and estimate an EHB close binary fraction of ~5% in $\omega$ Cen. This low fraction is in line with findings for other GGCs, but in sharp contrast to the situation in the field, where around 50% of the sdB stars reside in close binaries. Finally, the mass distribution derived is very similar for all three spectroscopic groups, however the average mass (0.38 Msun) is lower than that expected from stellar evolution theory. While this mass conundrum has previously been noted for EHB stars in $\omega$ Cen, it so far appears to be unique to that cluster.