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Appendix A: Stellar parameters and chemical abundances

Appendix B: Errors

The errors in the mass fractions were calculated using a Monte Carlo approach. We randomly drew 10⁵ values of the derived stellar abundances abundances following a Gaussian distribution centered on the derived abundance and with a sigma corresponding to the derived errors as listed in Tables A.1 and A.2. For each drawn set of [Si/H], [Mg/H], [O/H], and [C/H], we then computed the expected fractions. The distribution of the resulting values allowed us to derive the one-sigma error, as listed in Table 1.

We note that this procedure was done in a self consistent way. All the mass fractions were computed simultaneously for each set of input abundances. This is important because the resulting mass fraction values are correlated between themselves.

For Kepler-93, since the oxygen abundance was assumed to be solar (no O abundance could be derived from our data), we considered that the [O/H] has an uncertainty of 0.15 dex.

© ESO, 2015