The poor theoretical knowledge of the stellar mass loss history represents one of the main uncertainties in the computation of AGB stellar models. Low- and intermediate-mass stars lose the majority of their mass during the red giant branch (RGB) and the AGB phases. In 1D stellar evolutionary codes, the mass-loss rate during the RGB phase is commonly parameterized according to the formulation proposed by Reimers (1975):
2





where 





 is in units of M






 yr−1 and other quantities are in solar units. The uncertainty affecting this formula was originally quoted by Reimers to be at least a factor of two either way. Later, Fusi-Pecci  Renzini (1976) introduced a normalization constant in order to reproduce the horizontal branch morphology of globular clusters (





 = 0.4).10

10
FRUITY models adopt this value.
 Depending on the mass lost during the RGB phase (and thus on the value of 





), stars attain the AGB phase with different envelope masses. Thus, in principle, the RGB mass loss could have an effect on the subsequent AGB nucleosynthesis. Those effects are expected to be important for low-mass stars (M 





 1.5 M






) because they spend more time in the RGB phase than do larger masses. Moreover, their envelopes are thinner than in more massive stars, so even a small amount of material lost (e.g., 0.1 M






) can produce sizeable effects on the occurrence of TDU in the subsequent AGB phase (see, e.g., Straniero 2003). To properly determine the effects of RGB mass-loss rate on AGB nucleosynthesis (and thus on the solar s-only distribution), we calculate a set of M = 1.3 M






 models at different metallicities with 





. In Figure 10 we report the variations of the surface abundances (





) with respect to the corresponding FRUITY cases. We find that 





 are larger at low metallicities (in particular for the heaviest s-only isotopes). This is because at large metallicities this mass experiences a few TDU episodes, even using a milder RGB mass-loss rate. Thus, the final surface s-process enhancement is, in any case, low. By comparison, we also report data relative to a M = 2 





 Z = 10−2 ([Fe/H] = −0.15) model. The low variations found in this case confirm that for massive-enough AGB stars a reduced mass-loss rate during the RGB phase has practically no effect. In Figure 11 we report a GCE model computed with 





 in stars with M 





M






 (hereinafter the Reimers case). We find minor variations in the s-only distribution (see also Table 1), with slightly larger enhancements for the heaviest s-only isotopes (





). Our results reinforce the evidence that the major contributors to the solar system s-process inventory are AGB stars in the mass range (1.5–3.0) 





, as already inferred in Section 3. Their nucleosynthesis is strongly affected by the rate at which they lose mass during the AGB. A viable method to estimate AGB mass loss is based on the observed correlation with the pulsation period (Vassiliadis  Wood 1993). Because the evolution of the pulsation period depends on the variations of radius, luminosity, and mass, this relation provides a simple method to estimate the evolution of the mass-loss rate from basic stellar parameters. In our models, the AGB mass loss is determined according to a procedure similar to the one adopted by Vassiliadis  Wood (1993), but revising the mass loss–period and the period–luminosity relations, taking into account more recent infrared observations of solar-metallicity AGB stars (see Straniero et al. 2006 and references therein). It has been demonstrated that AGB mass-loss rates are mildly dependent on the metallicity (Groenewegen et al. 2007; Lagadec et al. 2008), and thus we applied the same period–mass loss relation for all AGB models present in the FRUITY database. Nevertheless, it is worth noting that, when a fixed period is defined, the observational data show quite a large scatter. In a period–mass loss plot, a theoretical curve constructed when reducing by a factor of two the mass-loss rate at a fixed period still lies within the observed spread (see Figure 8.10 of Cristallo 2006). This still holds for a mass-loss rate increased by a factor of two. In order to quantify the effects on the s-only distribution induced by a variation of the AGB mass-loss rate, we compute some AGB models with a milder and stronger period–mass loss relations. In Figure 12 we show the results on the final surface distributions of 2 M






 stellar models at various metallicities. In the plot, 





 represents the difference between models computed with the standard 





–period relation (Straniero et al. 2006) and the modified ones. Obviously, positive differences are obtained with a milder mass-loss rate, while negative differences with the stronger one. Heavy-element surface variations are below 0.1 dex (25%) for the whole s-process distribution, being slightly larger at low metallicity. Thus, we expect that a modified 





–period relation in the AGB phase will produce an almost rigid shift (upward or downward, depending on the adopted mass-loss law) of the s-process isotopes. In order to verify this statement, we compute a GCE model with a milder 





–period relation during the AGB phase (hereinafter the Mloss AGB case). The results are shown in Figure 13; the corresponding data are reported in Table 1. As expected, for s-only isotopes with A ≥ 96, there is an almost rigid upper shift of solar percentages (∼25%). In summary, a rigid shift (upward or downward) of the s-process isotopic inventory can be obtained by adopting a different prescription for the AGB mass-loss rate within the intrinsic observed scatter in the 





–period relation.
Citation: Straniero 2003
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