On the photometric signature of fast rotators

Rapidly rotating stars have been recently recognized as having a major role in the interpretation of colour-magnitude diagrams of young and intermediate-age star clusters in the Magellanic Clouds and in the Milky Way. In this work, we evaluate the distinctive spectra and distributions in colour-colour space that follow from the presence of a substantial range in effective temperatures across the surface of fast rotators. The calculations are inserted in a formalism similar to the one usually adopted for non-rotating stars, which allows us to derive tables of bolometric corrections as a function not only of a reference effective temperature, surface gravity and metallicity, but also of the rotational speed with respect to the break-up value, ω, and the inclination angle, i. We find that only very fast rotators (ω > 0.95) observed nearly equator-on (i > 45°) present sizable deviations from the colour-colour relations of non-rotating stars. In light of these results, we discuss the photometry of the ̃200-Myr-old cluster NGC 1866 and its split main sequence, which has been attributed to the simultaneous presence of slow and fast rotators. The small dispersion of its stars in colour-colour diagrams allows us to conclude that fast rotators in this cluster either have rotational velocities ω < 0.95, or are all observed nearly pole-on. Such geometric colour-colour effects, although small, might be potentially detectable in the huge, high-quality photometric samples in the post-Gaia era, in addition to the evolutionary effects caused by rotation-induced mixing.