6 Ages of SMR stars and the Age-metallicity relation

Figure 5: Diagram used to estimate ages for our program stars. Isochrones are from Bertelli et al. (1994). Full curves correspond to Z=0.02, and the dashed curves to Z=0.05 isochrones, respectively. Filled symbols denote stars with ${\rm [Fe/H]}\leq 0.20$ dex and open circles stars with ${\rm [Fe/H]}> 0.20$ dex. HD 32147 is too cool to show on the diagram

An age-metallicity relation among dwarf stars in the solar neighbourhood is a key observable that models of galactic chemical evolution must match. The most important recent studies include Edvardsson et al. (1993), Carraro et al. (1998), and Rocha-Pinto et al. (2000). The first two studies use the same [Fe/H], as derived in Edvardsson et al. (1993) from detailed abundance analysis. Carraro et al. (1998) make use of the age determinations done for Edvardsson et al. (1993) sample post Hipparcos (Ng & Bertelli 1998). Essentially, their data show a declining trend such that more metal-poor stars are older. However, the intrinsic scatter appears large in both age and [Fe/H] and a unique age-metallicity relation may not be present. The study by Rocha-Pinto et al. (2000) used a different technique to determine ages, chromospheric activity. They arrive at the conclusion that there exists a unique age-metallicity relation in the solar neighbourhood. The scatter in both age and metallicity are found to be small for all ages and metallicities (see their Fig. 13).

Figure 6: A comparison of our isochrone ages with the general age-metallicity relation derived by Rocha-Pinto et al. (2000). $\bullet$ refer to stars in this study, $\circ$ to stars from Gonzalez, see Table 8. $\times$ refers to the age-metallicity relation from Rocha-Pinto et al. where the error bars give the 1 $\sigma$ scatter around the mean [Fe/H] for each age bin

SMR stars are rare and therefore none of the studies discussed contain large numbers of them, in fact e.g. the Edvardsson et al. (1993) sample was selected with an upper limit in metallicity near 0.2 dex. Such a bias is not present in the Rocha-Pinto et al. (2000) sample, and they have a few stars of up to $\sim$0.3 dex (their Fig. 13). It is therefore valuable to derive ages for our small sample of stars and compare them to that of the general age-metallicity relations found in previous studies.

We have simply estimated the ages of the stars by plotting them in the $M_V - T_{\rm eff}$ plane and using the Bertelli et al. (1994) isochrones, Fig. 5. The ages were estimated by eye. The correct isochrones were chosen depending on the [Fe/H] for each star as derived in this study. In order to see if the age-metallicity relation appears unique also for the most metal-rich stars, we compare our data and the ages from the several papers by Gonzalez and co-workers, see Table 8, with the age-metallicity relation found in Rocha-Pinto et al. (2000) in Fig. 6.

A possible error source in the age determination of SMR stars is the presence of planets. Gonzalez (1998) noted that if one or several planets have been engulfed by a star, then its [Fe/H] may increase by up to around 0.10 dex. If this has happened, then the abundances and age for a polluted star will no longer represent it's true age and abundances. However, such a change in metallicity would still not turn a $\sim$10 Gyr star into a star of only a few Gyr, as required to fit into a general age-metallicity relation.

We note that our sample is not complete or in any other way well-defined. However, it proves that there also exist stars that are both very old and at the same time very metal-rich, also taking the errors in the ages into account. This casts doubts on the possibility of defining a one-to-one relation between age and metallicity among the solar neighbourhood stars.