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   \title{Calibration approach in the light of Gaia space mission}
   
   \subtitle{MARCS model based analysis of $\delta$ Eri}

   \author{V. Makaganiuk \inst{1}, A. Korn \inst{1}, U. Heiter \inst{1} and O. Kochukhov \inst{1}}

   \institute{Department of Physics and Astronomy, Division of Astronomy and Space Physics, Uppsala University, Box 515, 75120 Uppsala, Sweden\\
              \email{Vitaly.Makaganiuk@fysast.uu.se} \\
              \email{Andreas.Korn@fysast.uu.se}      \\
              \email{Ulrike.Heiter@fysast.uu.se}     \\
              \email{Oleg.Kochukhov@fysast.uu.se}}

   \date{Received XX XX, 2009; accepted XX XX, 2009}

% \abstract{}{}{}{}{} 
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  \abstract
  % context heading (optional)
  % {} leave it empty if necessary  
   {We investigate the possibility of using two spectral regions as independent and self-confirming information source for the derivation of fundamental parameters of the $\delta$ Eri star. It is also known that different stellar atmosphere models can introduce noticeable systematic effects in abundance derivation, so prior to the core analysis we have corrected a line list that was used in further analysis.}
  % aims heading (mandatory)
   {Compiling a list of atomic lines with calibrated oscillator strengths for cool stellar models to be used in future analysis of Gaia late-type stars. Judgement of the possible usage of optical region vs. infra-red in terms of deriving the information about fundamental stellar parameters and individual abundances of some chemical elements.}
  % methods heading (mandatory)
   {In order to minimize possible modelling effects we have calibrated \textit{gf} values of the spectral lines used in our analysis against the solar spectrum. For this purpose Spectroscopy Made Easy (SME) package along with MARCS model was utilized. The spectral synthesis method is underlying all our analysis process and calculations done under LTE assumption.}
  % results heading (mandatory)
   {It was found that that the results derived in the optical region of the spectrum fully confirm those, derived in the infra-red in spite of large quality difference between these regions. We also estimated the importance of the error in the initial parameters of the investigated object and their influence on the final result so it allowed us to conclude how accurately we can derive fundamental parameters and, particularly, abundances if the main tool for that is SME.}
  % conclusions heading (optional), leave it empty if necessary 
   {}

   \keywords{methods: data analysis -- techniques: spectroscopic -- stars: abundances}

   \maketitle

\section{Introduction}
	This work is done in the framework of the Gaia space mission. A satellite of the same name will be launched in 2011 and it will observe about 1 billion of objects in the Milky Way Galaxy, so investigations in the sense of astrometry are at the first place. Doing well on that stage we will get parallaxes, coordinates and proper motions of observed objects. For energy distribution studies in spectra two instruments are implemented on the satellite. One is a spectrophotometer that covers large wavelength regions and the second instrument is a medium-resolution spectrometer covering a short spectral region in infra-red (IR hereafter). Thanks to that the following scientific goals like galactic proper motions completed by rough radial velocities measurements become accomplishable.

	On the other hand classification course is rather reasonable as well as the determination of $T_{eff}$, log g and individual abundances of Ca and Fe for as many of the stars as possible. Observations will run for 5 years, so the amount of observed data will be huge. Then observed stellar spectra will be calibrated with known stars, so-called reference (or benchmark) stars, and implementation of new modelling methods will guide through this stage on behalf with understanding of reliability and accuracy of newly derived parameters. At the end of survey program, all spectra of the captured stars will be averaged over observational time scale. The quality of satellite spectra will be not so high as in case of ground-based observations and this fact plays significant role in data analysing, interpreting and, moreover, in drawing conclusion about evolution of our Galaxy. If we succeed with these attempts then it will lead to a new stage of scientific evolution in terms of understanding of the fundamental processes that take place in a surrounding world.

Gaia low resolution RVS spectrum lies in a region of $8470-8740$ \AA, which contains Ca II IR Triplet lines (hereafter CaT) and lines of some other chemical elements. To estimate the potential use of this region a number of stars were selected that statistically lie in Gaia$'$s field of view, that can be observed by ground-based telescopes with guaranteed quality of spectra. High quality of the data assumes correct reduction process that will allow us to derive consistent stellar parameters as it is discussed in this paper. Basing on the optical part of the spectrum we try to investigate the possibility to use it as a source of information about fundamental stellar parameters and individual abundances of Ca and Fe. If these parameters can be confirmed by a limited Gaia IR spectral range then we can benefit more in the future from RVS spectra not only in terms of radial velocities, but some other parameters. Ca and Fe were selected mainly because Gaia IR region contains some strong iron lines that are useful for analysis, but they are not so many and very prominent CaT lines. The latter ones will be used as a main source for radial velocities measurements.

	In Sect. 2 we describe the observations and mention some aspects of the reduction process. In Sect. 3 we focus on the preparation of the line list in terms of \textit{gf} calibrations using Kurucz solar spectrum and MARCS solar model. Sect. 4 contains some previously published results for $\delta$ Eri and analysis of derived fundamental parameters which ends up with a Sect. 5 where conclusions regarding this scientific work are presented. 

%__________________________________________________________________

\section{Observations and some reduction notes}

	Spectra were obtained on SARG spectrometer of TNG at La Palma, Spain. The highest expected resolving power is $R = 164000$ without image slicer and expected highest $S/N \sim 400$. Total instrument wavelength bandwidth is $3700-10000$ \AA. Observations were performed in two grism modes: blue with wavelength coverage $3600-5140$ \AA\ and red $4960-10110$ \AA, while we focused on two spectral regions: $5550-6750$ \AA\ and $8470-8740$ \AA. Reduction was performed with the help of REDUCE (Piskunov \& Valenti 2002). This a very flexible code with many options that can be set by a user. This means that in order to get the best output from the RAW data as possible, one has to have an experience of working with reduction software and understand the basic principles of instrumentation. Further we mention some distinctive aspects of the particular reduction process.
	
	REDUCE uses a cluster analysis method for order tracing. The best source for that is a flat field spectrum as it has no absorption lines and signal is rather high. It determines cluster groups accordingly to the signal level criterion and fits them with polynomial of certain degree. For all spectral orders we used $3^{rd}$ order polynomial since it provides the best fit of the each spectral order curvature. Corrected for pixel-to-pixel sensitivity variations and bias-subtracted spectra are being extracted then. To check the real quality of our data we have estimated the signal-to-noise ratio in the centre of each order for spectral regions of our interest. The result appeared to be somewhat lower than we expected. For the optical region the $S/N \sim 200-400$ and for the IR the $S/N \sim 70-90$.

	Extracted spectra were wavelength-calibrated based on ThAr spectrum. Wavelength scale let us to check the resolution of the data, which showed that starting from absolute order 110 ($\lambda_c = 5550$ \AA), where $R = 120000-130000$, it decreases to R = 85000-90000 in absolute order 66 ($\lambda_c = 9280$ \AA). Obviously the resolution is not as high as claimed but nevertheless still satisfactory for our scientific goals.

	The final problems we had to deal with were blending of spectral lines by absorption lines of the Earth$'$s atmosphere, so-called telluric lines, and fringing in the red orders. To eliminate telluric lines and straighten order profile a spectrum of the hot and rapidly rotating star (telluric standard) was used. This star was observed during the same night as the main target. In ideal case there should be no spectral lines in the spectrum of the telluric standard of its own. In our case we had to avoid division by the spectrum of the telluric star in spectral regions 5650-5760 \AA\ and 8470-8740 \AA\ because of the hydrogen lines presence in the spectrum of the standard. These regions were divided by the flat field instead. We tried to model the spectrum of telluric standard and divide it by the observed one but such way of Hydrogen lines removal was not as efficient as in case if we apply flat field division. The latter helped to reasonably reduce fringing as well as in case of using telluric standard.

\section{Preparation of the line list}

	The preparation and selection of spectral lines took most of the efforts as it is very important. Once we are ready with the line list it then can be applied to the set of benchmark stars, which are mainly belong to the late-type. In some sense we made a ground for our future investigations. Selection of the spectral lines was performed on a basis of Kurucz solar spectrum (Kurucz 2005) where we excluded some spectral lines, which were blended more than the criterion formulated as follows:

 \begin{equation}
   \frac{R_{cen}^{blend}}{R_{cen}^{line}} \geqslant 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 of the blend against the value of the main component that contributes to the spectral line formation. So 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 log \textit{gf} against the solar spectrum, using MARCS solar model (Gustafsson et al. 2008) with the help of SME package (Piskunov \& Valenti 1996), where the latter was rather modified since the times it was presented in the reference publication and allows performing advanced spectroscopic analysis. MARCS models in its turn, are the best available ones for the analysis of cool stellar atmospheres. Hence, we also used MARCS model in the analysis of $\delta$ Eri star, so it was very important to make the calibration procedure of oscillator strengths self-consistent and based on solar MARCS model. Ignoring this fact would lead to errors in abundance determination of the same order as the errors in log \textit{gf}, because there is a straight dependence between these parameters. The chemical elements of interest were Ca and Fe and log \textit{gf} calibrations were performed only for spectral lines of these species. 
	For synthesis calculation we used abundances from Asplund et al. 2005 and following solar parameters: $T_{eff} = 5777$ K, $log g = 4.44$, $\xi = 1.0 km/s$, $\zeta = 2.8 km/s$. Calibrated solar line list was applied to the spectrum of $\delta$ Eri which let us to exclude some more blended spectral lies from the analysis. It happens that if we go down on the temperature scale the number of spectral lines increases and some of them get blended. On Fig. 1 you can see the log \textit{gf} corrections derived from the solar spectrum for lines accepted for $\delta$ Eri analysis. All calculations are made under LTE assumption.

   \begin{figure}[t]
   \centering
   \includegraphics[width=\columnwidth]{Fig.1.eps}
   \caption{The scatter of log \textit{gf} corrections as a function of equivalent width. Black circles are corrections for Fe I lines and red ones are for Ca I.}
   \end{figure}
From the plot it can be clearly seen that the corrections we had to apply for the particular solar parameters and abundances are positive in majority and scattered around $\pm$ 0.4 dex. The goodness of the fit was estimated for every line by calculating standard deviation of the synthetic spectrum fit to the solar one. Even for the three outlying spectral lines, which belong to iron, that show required correction of log \textit{gf} larger than 0.4 dex the standard deviation values lie in range from 0.019 to 0.035 at the average $STD_{Fe} = 0.0956$. In other words, we may conclude that even for these seemingly large corrections we were able to achieve a good agreement between theoretical and observed profiles. On Fig. 2 you can see an example of the fit for one of the spectral lines that required oscillator strength correction by about 1 dex. The full list of Ca and Fe lines can be found in Table 1\& 2 respectively. The IR line list was calibrated in the same way as in the optical.

   \begin{figure}[t]
   \centering
   \includegraphics[angle=90,width=\columnwidth, clip]{Fig.2.ps}
   \caption{The fit of theoretical line profile (green line) after applied log \textit{gf} correction to the solar Fe I spectral line (black line).}
   \end{figure}

\begin{table*}[h]
\caption{Resulting log \textit{gf} corrections for Ca I lines that were used in spectral analysis of $\delta$ Eri.}
\centering
\begin{tabular}{l c c c c}
\hline\hline
Wavelength & log $\textit{gf}_{VALD}$ & log $\textit{gf}_{MARCS}$ & log $(\textit{gf}_{VALD}-\textit{gf}_{MARCS})$ & STD \\
\hline
5588.749 &   0.358	&   0.369  &   0.011  & 0.076 \\
5857.451 &   0.240	&   0.288  &   0.048  & 0.055 \\
5867.562 & $-1.570$	& $-1.573$ & $-0.003$ & 0.033 \\
6162.173 & $-0.090$	& $-0.147$ & $-0.057$ & 0.082 \\
6166.439 & $-1.142$	& $-1.091$ &   0.051  & 0.013 \\
6449.808 & $-0.502$	& $-0.411$ &   0.091  & 0.052 \\
6455.598 & $-1.340$	& $-1.308$ &   0.032  & 0.024 \\
6471.662 & $-0.686$	& $-0.586$ &   0.100  & 0.027 \\
6493.781 & $-0.109$	& $-0.035$ &   0.074  & 0.063 \\
6499.650 & $-0.818$	& $-0.696$ &   0.122  & 0.011 \\
\hline
\end{tabular}
\end{table*}

\begin{table*}
\caption{Same as Table 1 but for Fe I lines.}
\centering
\begin{longtable}{l c c c c}
\hline\hline
Wavelength & log $\textit{gf}_{VALD}$ & log $\textit{gf}_{MARCS}$ & log $(\textit{gf}_{VALD}-\textit{gf}_{MARCS})$ & STD \\
\hline
5554.882  & $-0.440$ & $-0.149$ &   0.291  & 0.039 \\
5560.207  & $-1.190$ & $-1.029$ &   0.161  & 0.015 \\
5569.618  & $-0.486$ & $-0.510$ & $-0.024$ & 0.000 \\
5576.089  & $-1.000$ & $-0.860$ &   0.140  & 0.009 \\
5577.025  & $-1.550$ & $-1.458$ &   0.092  & 0.020 \\
5584.764  & $-2.320$ & $-2.144$ &   0.176  & 0.120 \\
5587.574  & $-1.850$ & $-1.601$ &   0.249  & 0.056 \\
5607.664  & $-2.270$ & $-2.177$ &   0.093  & 0.012 \\
5618.631  & $-1.276$ & $-1.261$ &   0.015  & 0.019 \\
5619.587  & $-1.700$ & $-1.451$ &   0.249  & 0.058 \\
5624.022  & $-1.480$ & $-1.118$ &   0.362  & 0.054 \\
5633.946  & $-0.270$ & $-0.158$ &   0.112  & 0.048 \\
5635.822  & $-1.890$ & $-1.551$ &   0.339  & 0.028 \\
5636.696  & $-2.610$ & $-2.491$ &   0.119  & 0.017 \\
5638.262  & $-0.870$ & $-0.731$ &   0.139  & 0.007 \\
5640.307  & $-1.374$ & $-1.584$ & $-0.210$ & 0.034 \\
5651.469  & $-2.000$ & $-1.751$ &   0.249  & 0.007 \\
5652.318  & $-1.950$ & $-1.748$ &   0.202  & 0.022 \\
5653.865  & $-1.640$ & $-1.360$ &   0.280  & 0.037 \\
5655.176  & $-0.640$ & $-0.454$ &   0.186  & 0.062 \\
5661.345  & $-1.736$ & $-1.830$ & $-0.094$ & 0.022 \\
5662.516  & $-0.573$ & $-0.356$ &   0.217  & 0.003 \\
5677.684  & $-2.700$ & $-2.625$ &   0.075  & 0.006 \\
5691.497  & $-1.520$ & $-1.400$ &   0.120  & 0.024 \\
5696.089  & $-1.720$ & $-1.860$	& $-0.140$ & 0.009 \\
5698.020  & $-2.680$ & $-2.666$	&   0.014  & 0.024 \\
5704.733  & $-1.409$ & $-1.190$	&   0.219  & 0.016 \\
5705.464  & $-1.355$ & $-1.433$	& $-0.078$ & 0.026 \\
5712.131  & $-1.990$ & $-2.003$	& $-0.013$ & 0.025 \\
5717.833  & $-1.130$ & $-0.973$	&   0.157  & 0.049 \\
5730.854  & $-1.445$ & $-1.808$	& $-0.363$ & 0.013 \\
5731.762  & $-1.300$ & $-1.066$	&   0.234  & 0.015 \\
5732.295  & $-1.560$ & $-1.389$	&   0.171  & 0.037 \\
5741.846  & $-1.854$ & $-1.610$ &   0.244  & 0.025 \\
5752.032  & $-1.177$ & $-0.843$ &   0.334  & 0.025 \\
5753.121  & $-0.688$ & $-0.690$ & $-0.002$ & 0.002 \\
5760.344  & $-2.490$ & $-2.433$ &   0.057  & 0.012 \\
5775.081  & $-1.298$ & $-1.040$ &   0.258  & 0.036 \\
5778.453  & $-3.430$ & $-3.459$ & $-0.029$ & 0.028 \\
5784.657  & $-2.532$ & $-2.543$ & $-0.011$ & 0.046 \\
5793.913  & $-1.700$ & $-1.581$ &   0.119  & 0.047 \\
5804.463  & $-2.040$ & $-1.866$ &   0.174  & 0.049 \\
5809.217  & $-1.840$ & $-1.753$ &   0.087  & 0.041 \\
5814.805  & $-1.970$ & $-1.800$ &   0.170  & 0.029 \\
5835.098  & $-2.370$ & $-2.097$ &   0.273  & 0.015 \\
5852.217  & $-1.330$ & $-1.174$ &   0.156  & 0.009 \\
5855.076  & $-1.478$ & $-1.508$ & $-0.030$ & 0.020 \\
5856.083  & $-1.328$ & $-1.532$ & $-0.204$ & 0.022 \\
5859.586  & $-0.419$ & $-0.457$ & $-0.038$ & 0.013 \\
5883.813  & $-1.360$ & $-1.071$ &   0.289  & 0.004 \\
5905.671  & $-0.730$ & $-0.715$ &   0.015  & 0.022 \\
5929.667  & $-1.410$ & $-1.173$ &   0.237  & 0.023 \\
5930.173  & $-0.230$ & $-0.189$ &   0.041  & 0.008 \\
5976.777  & $-1.243$ & $-1.118$ &   0.125  & 0.038 \\
5983.680  & $-1.468$ & $-0.464$ &   1.004  & 0.035 \\
6003.010  & $-1.120$ & $-0.963$ &   0.157  & 0.013 \\
6007.960  & $-0.597$ & $-0.602$ & $-0.005$ & 0.042 \\
6008.556  & $-0.986$ & $-0.707$ &   0.279  & 0.021 \\
6012.238  & $-4.038$ & $-3.857$ &   0.181  & 0.068 \\
6024.079  & $-0.120$ &   0.067  &   0.187  & 0.009 \\
6027.051  & $-1.089$ & $-1.062$ &   0.027  & 0.064 \\
6078.491  & $-0.321$ & $-0.129$ &   0.192  & 0.039 \\
6078.999  & $-1.120$ & $-0.963$ &   0.157  & 0.024 \\
6082.708  & $-3.573$ & $-3.539$ &   0.034  & 0.015 \\
6093.643  & $-1.500$ & $-1.315$ &   0.185  & 0.021 \\
6094.364  & $-1.940$ & $-1.552$ &   0.388  & 0.019 \\
6127.906  & $-1.399$ & $-1.352$ &   0.047  & 0.037 \\
6136.615  & $-1.400$ & $-1.393$ &   0.007  & 0.007 \\
6136.993  & $-2.950$ & $-2.916$ &   0.034  & 0.018 \\
6151.617  & $-3.299$ & $-3.245$ &   0.054  & 0.015 \\
6173.334  & $-2.880$ & $-2.816$ &   0.064  & 0.011 \\
6187.987  & $-1.720$ & $-1.609$ &   0.111  & 0.031 \\
6200.313  & $-2.437$ & $-2.326$ &   0.111  & 0.024 \\
6213.429  & $-2.482$ & $-2.497$ & $-0.015$ & 0.006 \\
6220.776  & $-2.460$ & $-2.309$ &   0.151  & 0.023 \\
6226.730  & $-2.220$ & $-2.074$ &   0.146  & 0.022 \\
6240.310  & $-2.083$ & $-2.186$ & $-0.103$ & 0.023 \\
6240.645  & $-3.233$ & $-3.263$ & $-0.030$ & 0.018 \\
6246.317  & $-0.733$ & $-0.771$ & $-0.038$ & 0.002 \\
6252.554  & $-1.687$ & $-1.658$ &   0.029  & 0.011 \\
6265.131  & $-2.550$ & $-2.497$ &   0.053  & 0.020 \\
6270.222  & $-2.464$ & $-2.553$ & $-0.089$ & 0.022 \\
6271.276  & $-2.703$ & $-2.725$ & $-0.022$ & 0.020 \\
6297.792  & $-2.740$ & $-2.693$ &   0.047  & 0.021 \\
6301.500  & $-0.718$ & $-0.465$ &   0.253  & 0.013 \\
6302.494  & $-0.973$ & $-1.048$ & $-0.075$ & 0.023 \\
6330.838  & $-1.740$ & $-1.156$ &   0.584  & 0.019 \\
6335.328  & $-2.177$ & $-2.232$ & $-0.055$ & 0.008 \\
6336.823  & $-0.856$ & $-0.836$ &   0.020  & 0.003 \\
6338.876  & $-1.060$ & $-0.899$ &   0.161  & 0.021 \\
6380.743  & $-1.376$ & $-1.204$ &   0.172  & 0.003 \\
6385.716  & $-1.910$ & $-1.799$ &   0.111  & 0.007 \\
6392.538  & $-4.030$ & $-3.945$ &   0.085  & 0.004 \\
6393.600  & $-1.432$ & $-1.495$ & $-0.063$ & 0.008 \\
6408.018  & $-1.018$ & $-0.806$ &   0.212  & 0.016 \\
6411.647  & $-0.595$ & $-0.600$ & $-0.005$ & 0.009 \\
6419.942  & $-0.240$ & $-0.248$ & $-0.008$ & 0.005 \\
6430.844  & $-2.006$ & $-1.993$ &   0.013  & 0.001 \\
6481.869  & $-2.984$ & $-2.903$ &   0.081  & 0.027 \\
6494.999  & $-1.273$ & $-1.260$ &   0.013  & 0.004 \\
6496.466  & $-0.570$ & $-0.528$ &   0.042  & 0.003 \\
6653.850  & $-2.520$ & $-2.390$ &   0.130  & 0.013 \\
6703.566  &	$-3.160$ & $-2.997$ &   0.163  & 0.029 \\
6710.316  &	$-4.880$ & $-4.795$ &   0.085  & 0.023 \\
6713.743  &	$-1.600$ & $-1.396$ &   0.204  & 0.012 \\
6725.353  &	$-2.300$ & $-2.185$ &   0.115  & 0.005 \\
6726.666  & $-1.133$ & $-0.989$ &   0.144  & 0.033 \\
6733.150  & $-1.580$ & $-1.406$ &   0.174  & 0.016 \\
6739.520  & $-4.794$ & $-4.872$ & $-0.078$ & 0.012 \\
\hline
\end{longtable}
\end{table*}

\section{Analysis}

	Since the analysis of $\delta$ Eri was planned to be based on spectral synthesis method we focused on those publications that used the same method for derivation of the fundamental parameters. This star is well studied so the published results were rather reliable in sense of scatter of the parameters. The summary of the previously published results can be found in the Table 3.
	
\begin{table*}[h]
\caption{Results from some previous publications related to $\delta$ Eri.}
\centering
\begin{tabular}{c c c c c}
\hline\hline
$T_{eff}$ & log g & $[M/H]$ & $\xi$ & Reference \\
\hline
5074 $\pm$ 60 & 3.77 $\pm$ 0.16 & 0.13 $\pm$ 0.08 & 1.08 $\pm$ 0.06 & Gilli et al 2006   \\
5100          & 3.8             & 0.18            & 0.60            & Luck \& Heiter 2006 \\
\hline
\end{tabular}
\end{table*}
One of the highest priorities in our analysis was accuracy, so in that respect the selection of starting fundamental parameters was also important. We did not use metallicity parameter and set it to zero, since the main attention was focused on individual abundances. Surface gravity parameter was taken from Ramirez et al 2007 because it was derived from latest parallax value of $\pi=110.61 \pm 0.22$ mas, hence, more precise. Summarizing all this the fundamental parameters we assumed for the first synthesis calculation were following: $T_{eff}=5070$ K, $log g=3.78$, $\xi=1.08\ km/s$ and $\chi=0\ km/s$.

	The main tool we used, SME, is very flexible and allows fitting of many spectral parameters at the same time. Basically it finds an optimal fit to the data by minimizing the $\xi^2$, i. e. minimizing the difference between synthetic spectrum and observed data. This is done by selecting desired spectral regions and setting spectral parameters of interest as free. The code changes these free parameters and re-calculates the synthesis until the convergence is achieved. If the initial parameters are not known with certain confidence it is better not to set more than two free parameters, otherwise the result may be completely wrong because of simple correlation between tuned parameters.

	We started with finding values of turbulent and radial velocities. The latter was set to be free throughout all calculation runs, since it does not correlate with other fundamental parameters. The log g was fixed, because the values derived from parallax is rather precise and does not need to tuned. The rotational velocity was set to zero and was not tuned because as it was shown by (A. Korn?) the macroturbulent velocity dominates in atmospheres of such stars and there is no need to account for v sin i as they are slow rotators also. Preliminary synthesis calculation resulted in $T_{eff}=5026$ K, $\xi=1\ km/s$ and $\chi=3.5\ km/s$. The radial velocity was found to be $v_{rad}=-3.5 km/s$.
	
	To estimate the effect, which can be produced by setting wrong initial parameters we decided to run several tests, where the effective temperature was perturbed by $\pm$ 200 K and individual abundances of iron and calcium by $\pm$ 0.2 dex. For more precise determination of $T_{eff}$ we have included 4 Fe II spectral lines free of blends and their log \textit{gf}s were taken from Melendez \& Barbuy 2009. Derived $T_{eff}=5035 \pm 32$ K was used for further calculations in the IR region, where no sufficient information for deriving effective temperature was available. The individual abundances of Ca and Fe are $-5.67 \pm 0.03$ dex and $-4.48 \pm 0.03$ dex respectively. These parameters were derived for the optical region of $5550-6750 \AA$ based on 109 Fe I lines and 10 of Ca I.
	
	Talking about importance of oscillator strengths correction we would like to demonstrate it on the example of IR region. If one takes \textit{gf}s as they are provided by VALD it may alter additional errors in abundance determination. In our case this resulted in 0.04 and 0.09 dex abundance difference for Ca and Fe respectively. Thereby, the IR line list was also corrected in terms of oscillator strengths in the same way it was done for the optical. We derive $\varepsilon(Ca)=-5.65 \pm 0.01$ dex and $\varepsilon(Fe)=-4.47 \pm 0.03$ dex which seem to be in a good agreement between the two spectral regions. All results, derived in both regions can be found in Table 4.
	
\section{Conclusions}

	Summarizing this work, we want to point out, that such analysis was performed for the first time in the framework of the Gaia space mission. We mainly focused on development of the methodology which must be robust and effective, because there is still a number of benchmark stars that have to be processed in the same way as $\delta$ Eri, thus widening the application possibility in a sense of statistics. It is very challenging to see how this method will work with stars, that are 1000 K cooler, for instance, than our current object. The situation may look not so promising there due to the problems with continuum normalization and more severe blending. But still it is a subject of future discussions.
	
	Here we pointing out, that this method is working and gives a good confirmation for the individual abundances independently derived from optical and Gaia RVS range even in LTE. The agreement is quite impressive and of the order of 0.01 dex within the errors. But this result was achieved based on high resolution spectral material, while Gaia spectra will not be of such good quality.
Keeping all that in mind, our recommendations would be following: test this methodology against all benchmark stars, planned for observations. This will show the possible limitations of such data treatment. If this will turn out to be a success, then one can approach closer to the reality in a sense that the IR part of the spectrum can be degraded in quality down to that of Gaia. On that stage it may cause some problems and the direct way we used in high resolution spectroscopy will not be applicable, so the introduction of some corrections or weights will be needed. Finally, one of the future tasks will be implementation of 3D model atmospheres and synthesis calcuation under NLTE assumption.
	
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