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A fraction of the extreme horizontal branch stars of globular clustersexhibit a periodic light variability that has been attributed to rotationalmodulation caused by surface spots. These spots are believed to be connected toinhomogeneous surface distribution of elements. However, the presence of suchspots has not been tested against spectroscopic data. We analyzed thephase-resolved ESO X-shooter spectroscopy of three extreme horizontal branchstars that are members of the globular cluster $\omega$ Cen and also displayperiodic light variations. The aim of our study is to understand the nature ofthe light variability of these stars and to test whether the spots canreproduce the observed variability. Our spectroscopic analysis of these starsdid not detect any phase-locked abundance variations that are able to reproducethe light variability. Instead, we revealed the phase variability of effectivetemperature and surface gravity. In particular, the stars show the highesttemperature around the light maximum. This points to pulsations as a possiblecause of the observed spectroscopic and photometric variations. However, suchan interpretation is in a strong conflict with Ritter's law, which relates thepulsational period to the mean stellar density. The location of the $\omega$Cen variable extreme horizontal branch stars in HR diagram corresponds to anextension of PG 1716 stars toward lower temperatures or blue, low-gravity,large-amplitude pulsators toward lower luminosities, albeit with much longerperiods. Other models of light variability, namely, related to temperaturespots, should also be tested further. The estimated masses of these stars inthe range of $0.2-0.3\,M_\odot$ are too low for helium-burning objects.

The nature of medium-period variables on the extreme horizontal branch I. X-shooter study of variable stars in the globular cluster $\omega$ Cen