Δ[Na/Fe]ini (colour-coded) as a function of initial stellar mass and initial helium mass fraction for the highest [Fe/H] values considered in this study. Grey horizontal lines denote constant values of Na enrichment Δ[Na/Fe]ini. The black, green, and blue full lines separate the stars that climb the AGB (to the right of the lines) from those that do not (left), with the shaded areas corresponding to error bars of 0.005 M⊙ related to the mass step of the model grid. The black limit corresponds to the most stringent definition of the AGB (a star undergoes at least two thermal pulses), while the green and blue curves are for the C13 definition of the AGB (i.e., early-AGB only is included). The black and green cases on the one hand and the blue case on the other hand are obtained assuming a value of η of 0.5 and 0.65, respectively, in the Reimers mass loss prescription. The black dashed lines are isochrones representing the ages at the end of the helium-burning (in Gyr). The white area corresponds to the domain where stellar models have an age higher than 13.8 Gyr at the end of the helium-burning phase or do not enter that phase.
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