Evolution of surfacepolluted stars and age determination

Finally, it would be worth briefly mentioning another important stellar parameter: the age. Very intriguing as well as puzzling is the origin of "old metal-rich stars" (e.g. Feltzing & Gonzalez 2001), the existence of which apparently contradicts the galactic chemical evolution. While this might partly be attributed to an inhomogene-ity of the gas from which stars formed, it is unlikely that all cases can be explained in this manner. Here, attention should be paid to two points that are actually related to each other, i.e. (i) the reality of the (spectroscopically derived) metallicity and (ii) the reliability of the age (determined mostly with the help of theoretical stellar evolutionary tracks).

Regarding the first point, we must recall that a great many planet-harboring stars are metal-rich and the reason for this fact has been a controversial matter throughout this decade (e.g. Gonzalez 2003): one explanation is the hypothesis of so-called "surface enrichment" due to infall of H-depleted solid planetesimals; and the other is that of the "primordial origin" (i.e. formation of planets favors metal-rich environments). Although the latter interpretation appears to be more advantageous than the former on the basis of currently accumulated observational facts (e.g. Ecuvillon et al. 2006 and references therein), the possibility of surface-polluted enrichment may still be worthy of consideration. In this case, the metal-richness is confined entirely to the surface convection zone, while the metallicity of the stellar interior remains normal.

On the basis of a working hypothesis that the high metallicity of metal-rich stars is of enrichment origin and merely superficial, Y. Katsuta and M. Fujimoto at Hokkaido University investigated the evolution of such surface-polluted stars, in order to assess errors in the age determination expected when the "ordinary" tracks of homogeneous metallicity are inadequately used. The results of some representative cases (Y. Katsuta, private communication) are depicted in Figure 32.10(a); two consequences have tentatively been concluded.

• If the polluted track and the standard homogeneous track with the same surface (enriched) metallicity (e.g. Z = 0.04) are compared with each other, the former is situated on the bluer side relative to the latter; accordingly, the true age of a superficially metal-rich star may be older than that obtained from the standard tracks.

• Such a superficially metal-enriched star would be situated below (leftward of) the main sequence (like subdwarfs), so it would be impossible to determine its age by using the ordinary tracks/isochrones. Therefore, such "subdwarf-like metal-rich stars" (should they be found) may be promising candidates for surface-polluted stars.

Unfortunately, the former implication does not solve the problem of old metal-rich stars; i.e. the direction of the age correction is if anything the opposite. Also, in our check on the positions of the HR diagram for the SMR ([Fe/H] > 0.2) stars selected from Valenti & Fisher's (2005) extended sample we could not confidently nominate such clear subdwarf-like stars (Figure 32.10(b)). Accordingly, we can not state that such a surface-polluted model (at least in the present simple version) successfully applies for explaining the problems currently being confronted.1 This,

-Girardi et al. (2000) [Fe/H] = +0.20 (Z = 0.03) tracks (for various masses)

-Girardi et al. (2000) [Fe/H] = +0.20 (Z = 0.03) tracks (for various masses)

Figure 32.10. (a) Evolutionary tracks for homogeneous-metallicity (normal) stars and surface-polluted stars, calculated by Katsuta & Fujimoto (in preparation) for the representative M = 0.8M0 and 1.0M0 cases. The numbers marked on each of the normal tracks, where the dotted lines are for M = 0.8M0 as the dashed lines are for M = 1.0M0, are the corresponding Z values (metallicity). The tracks of the surface-polluted stars are shown by the solid lines. (b) Super-metal-rich stars ([Fe/H] > 0.2) selected from Valenti & Fisher's (2005) sample plotted on the theoretical HR diagram, where Girardi et al.'s (2000) metal-rich (Z = 0.03) tracks for various masses from 0.8M0 to 1.7M0 with a step of 0.1 M0 are also shown. The open and filled symbols denote planet-host stars and non-planet-host stars, respectively.

in turn, suggests that the enrichment scenario may be less promising for the origin of high metallicity in planet-harboring stars.

6 Conclusion

(a) For F-G stars with Teff higher than ~5,000 K and K giants, the NLTE effect is not so significant in spite of a marginal sign of overionization and LTE would still remain a practically useful approximation.

(b) Meanwhile, use of LTE had better be avoided for K dwarfs with Teff < 5,000 K because classical modeling is likely to break down (is this activity-related?).

(c) Regarding the metallicity of the Hyades cluster, our analysis of G dwarfs suggested a preference for the "high" scale of [Fe/H] ~ 0.2.

(d) The age of a polluted (superficially) metal-rich star derived from standard tracks would be underestimated, and it seems difficult to explain the mystery of old metal-rich stars by invoking this kind of model (unless other parameters are tuned appropriately).

(e) A pollution-enriched star would be detected as a "subdwarf-like" metal-rich star, though such candidates appear to be rather few, if any exist at all.

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