
A large effort was put on the preparation and selection of suitable spectral lines, both in the optical and in the RVS spectral regions. The optical region was selected in such limits (see Sect. 3), which are widely used in the literature for the late-type stars because it is optimal in terms of line density (a large number of lines, not too dense and hence unblended, are available). The line list in the optical region compiled here represents our ``standard set of spectral lines'' mentioned above and is to be applied to the full set of benchmark stars with minor adaptations for earlier spectral types. The selection of the spectral lines was performed on the basis of line data extracted from the VALD and the Kurucz solar spectrum \citep{2005MSAIS...8..189K}. We excluded those spectral lines which were blended according to the criterion formulated as follows:

 \begin{equation}
    \frac{R_{cen}^{blend}}{R_{cen}^{line}} \geq 0.2 \,
 \end{equation}

$R_{cen}$ here is the central depth of the spectral line returned in the VALD line list. We compare this value for the blend with the value of the main component that contributes to the spectral feature. Thus, all lines for which this ratio was about 20\% or less we counted as appropriate for the analysis.

This line list was calibrated in terms of oscillator strengths $\log gf$ against the solar spectrum, using a MARCS solar model \citep{Gust:08} with the help of the SME package \citep{Vale:96,2005ApJS..159..141V}. Note, that we also used MARCS models in the analysis of $\delta$ Eri, ensuring consistency of the calibration procedure of oscillator strengths and the abundance analysis.  All calculations are made under LTE assumption. The chemical elements of interest are Ca and Fe and line selection and $\log gf$ calibrations were performed only for spectral lines of these species. All line data apart from $\log gf$ are from the VALD database.

For the synthesis calculation we used the solar abundances from \citet{2005ASPC..336...25A}, $\log\epsilon$(Ca)=6.31 and $\log\epsilon$(Fe)=7.45, and the following solar parameters: \Teff = 5777~K, \logg = 4.44, $\xi$ = 1.0~\kms , $\zeta$ = 2.8\,\kms, where $\xi$ and $\zeta$ are the micro- and macroturbulence parameters, respectively.
For the analysis of $\delta$ Eri, we had to exclude a few spectral lines from the solar-calibrated line list. Due to the lower temperature of $\delta$ Eri compared to the Sun, the number and strength of spectral lines increases, leading to more blends.
The final line lists contain 10 Ca~I and 109 Fe~I lines in the optical wavelength region, which can be found in Table \ref{tab:CaFeopt}.

   \begin{figure}[t]
   \centering
   \includegraphics[angle=90,width=\columnwidth]{Fig2.ps}
   \caption{The $\log gf$ corrections for the optical wavelength region as a function of calculated equivalent width. Rhomb symbols are the corrections for Fe I lines and triangles show corrections for Ca I.}
   \label{fig:gfcorr}
   \end{figure}

In Fig.~\ref{fig:gfcorr} $\log gf$ corrections derived from the solar spectrum for lines in the optical wavelength region adopted for the $\delta$ Eri analysis are dsiplayed.
From the plot it can be clearly seen that the corrections we had to apply for the particular solar parameters and abundances are mainly positive, with a mean correction of +0.11$\pm0.16$\,dex for Fe~I and +0.05$\pm0.05$\,dex for Ca~I.
The goodness of the fit was estimated for every line by calculating the standard deviation of the synthetic spectrum fit to the solar observation ($\sigma$ in Table \ref{tab:CaFeopt}). Even for the three Fe~I lines, which show the largest required correction of $\log gf$ ($\gtrsim$0.4~dex), the standard deviation values lie in range from 0.019 to 0.035, which is comparable to the average of the $\sigma$ values for all optical Fe~I lines (0.023). In other words, we may conclude that even for these seemingly large corrections we were able to achieve a reasonable agreement between theoretical and observed profiles.

\begin{table}[h]
   \caption{\label{tab:FeIir} Resulting $\log gf$ corrections for Fe I lines in the IR that were used for the spectral analysis of $\delta$ Eri.}
\centering
\begin{tabular}{l r r r r r}
\hline\hline
Wavelength, & \textit{E}, & $\log gf_{\rm MARCS}$ & $ \log gf_{\rm MARCS}$ & $\sigma$ & $\log \gamma_{6}$ \\
  \AA       & eV  &                       & $- \log gf_{\rm VALD}$ &          &                  \\
\hline
8514.0723 & 2.198 & $-2.362$ & -0.218 & 0.002 & $-7.361$ \\
8515.1084 & 3.018 & $-2.035$ & -0.161 & 0.001 & $-7.322$ \\
8526.6689 & 4.913 & $-0.613$ & -0.095 & 0.001 & $-6.977$ \\
8571.8037 & 5.010 & $-1.061$ & -0.030 & 0.034 & $-7.480$ \\
8582.2568 & 2.990 & $-2.078$ & -0.227 & 0.026 & $-7.780$ \\
8592.9512 & 4.956 & $-0.792$ & -0.051 & 0.001 & $-6.504$ \\
8611.8037 & 2.845 & $-2.076$ & -0.013 & 0.227 & $-7.900$ \\
8613.9404 & 4.988 & $-1.065$ & -0.043 & 0.033 & $-7.470$ \\
8616.2803 & 4.913 & $-0.881$ & -0.069 & 0.018 & $-7.520$ \\
8621.6006 & 2.949 & $-2.235$ & -0.201 & 0.019 & $-7.780$ \\
8674.7461 & 2.831 & $-1.850$ & -0.213 & 0.005 & $-7.371$ \\
8688.6260 & 2.176 & $-1.208$ & -0.059 & 0.016 & $-7.691$ \\
\hline
\end{tabular}
\end{table}

\addtocounter{table}{1}

