# On the photometric signature of fast rotators

## TL;DR

This paper investigates how rapid stellar rotation affects the spectral and photometric properties of stars, providing models to interpret observations of star clusters and the impact of rotation on their colour-magnitude diagrams.

## Contribution

It introduces a formalism to compute bolometric corrections for fast rotators considering rotation speed and inclination, and analyzes their photometric signatures in star clusters.

## Key findings

- Only very fast rotators observed nearly equator-on show significant deviations in colour-colour diagrams.
- The small dispersion in NGC 1866's stars suggests fast rotators are either slow or observed nearly pole-on.
- Geometric effects of rotation on photometry are subtle but potentially detectable with high-quality data.

## Abstract

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, $\omega$, and the inclination angle, $i$. We find that only very fast rotators ($\omega>0.95$) observed nearly equator-on ($i>45^\circ$) present sizable deviations from the colour-colour relations of non-rotating stars. In light of these results, we discuss the photometry of the $\sim$ 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 allow us to conclude that fast rotators in this cluster either have rotational velocities $\omega<0.95$, 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.