Evolution of long-lived globular cluster stars III. Effect of the
  initial helium spread on the position of stars in a synthetic
  Hertzsprung-Russell diagram
  Context. Globular clusters host multiple populations of long-lived low-mass
stars whose origin remains an open question. Several scenarios have been
proposed to explain the associated photometric and spectroscopic peculiarities.
They differ, for instance, in the maximum helium enrichment they predict for
stars of the second population, which these stars can inherit at birth as the
result of the internal pollution of the cluster by different types of stars of
the first population. Aims. We present the distribution of helium-rich stars in
present-day globular clusters as it is expected in the original framework of
the fast-rotating massive stars scenario (FRMS) as first-population polluters.
We focus on NGC 6752. (to be continued)
