On the determination of the He abundance distribution in globular clusters from the width of the main sequence

One crucial piece of information to study the origin of multiple stellar populations in globular clusters is the range of initial helium abundances Delta Y amongst the sub-populations hosted by each cluster. These estimates are commonly obtained by measuring the width in colour of the unevolved main sequence in an optical colour-magnitude diagram (CMD). The measured colour spread is then compared with predictions from theoretical stellar isochrones with varying initial He abundances to determine Delta Y. The availability of UV/optical magnitudes, thanks to the Hubble Space Telescope UV Legacy Survey of Galactic GCs project, will allow the homogeneous determination of Delta Y for a large Galactic globular cluster sample. From a theoretical point of view, accurate UV CMDs can efficiently disentangle the various sub-populations, and main sequence colour differences in the ACS F606W - (F606W - F814W) diagram allow an estimate of Delta Y. We demonstrate that from a theoretical perspective, the (F606W - F814W) colour is an extremely reliable He-abundance indicator. The derivative dY/d(F606W - F814W), computed at a fixed luminosity along the unevolved main sequence, is largely insensitive to the physical assumptions made in stellar model computations, being more sensitive to the choice of the bolometric correction scale, and is only slightly dependent on the adopted set of stellar models. From a theoretical point of view, the (F606W - F814W) colour width of the cluster main sequence is therefore a robust diagnostic of the Delta Y range.