Evolution of long-lived globular cluster stars I. Grid of stellar models with helium enhancement at [Fe/H] =-1.75

Context. Our understanding of the formation and early evolution of globular clusters (GCs) has been totally overthrown with the discovery of the peculiar chemical properties of their long-lived host stars. Aims. As a consequence, the interpretation of the observed color-magnitude diagrams and of the properties of the GC stellar populations requires the use of stellar models computed with relevant chemical compositions. Methods. We present a grid of 224 stellar evolution models for low-mass stars with initial masses between 0.3 and 1.0 M-circle dot and initial helium mass fraction between 0.248 and 0.8 computed for [Fe/H] = -1.75 with the stellar evolution code STAREVOL. This grid is made available to the community. Results. We explore the implications of the assumed initial chemical distribution for the main properties of the stellar models: evolution paths in the Hertzsprung-Russel diagram (HRD), duration and characteristics of the main evolutionary phases, and the chemical nature of the white dwarf remnants. We also provide the ranges in initial stellar mass and helium content of the stars that populate the different regions of the HRD at the ages of 10 and 13.4 Gyr, which are typical for Galactic GCs.