χ² obtained from the evaluation of a simulated spectrum at [M/H]₀= [Fe/H]₀= −3.8 (marked with a vertical dotted line) compared with synthetic spectra over a range of metallicities [M/H] (from −5.0 to −2.5 with a step of 0.1 dex). The blue line shows the resulting χ² curve for a simulation with S/N = 30, and the red line applies to S/N = 80. The two black dotted lines indicate the linear fits up to the [M/H]₀ corresponding to the minimum χ², from which the slope and its uncertainty are derived.