
\documentclass[journal]{rmaa}


\newcommand{\casitiny}{\fontsize{6}{7}\selectfont}


\title{FUNDPAR: A program for Deriving Fundamental Parameters from Equivalent Widths}


\author{C. Saffe\affil{Instituto de Ciencias Astron\'omicas, de la Tierra y del
Espacio (ICATE), San Juan, Argentina}}

\altaffiltext{1}{{\tt http://icate-conicet.gob.ar/saffe/fundpar/}.}

\shortauthor{Saffe} 

\shorttitle{A program for deriving fundamental parameters}


\listofauthors{C.~Saffe}

\indexauthor{Saffe, C.}


\fulladdresses{
\item C. Saffe: Instituto de Ciencias Astron\'omicas, de la Tierra y del Espacio (ICATE), C.C 467, 5400, San Juan, Argentina. 
Member of the Carrera del Investigador Cient\'ifico, Consejo Nacional de Investigaciones Cient\'ificas y T\'ecnicas (CONICET)
de la Rep\'ublica Argentina (csaffe@icate-conicet.gob.ar).}


\SetYear{2010}
\ReceivedDate{2 July 2010}
\AcceptedDate{14 September 2010}
\SetVolume{47}
\SetFirstPage{1}


\abstract{We implemented a Fortran code that determines fundamental parameters of solar type stars from a list of Fe line equivalent 
widths. The solution should verify three conditions in the standard method: ionization equilibrium, excitation equilibrium and 
independence between metallicity and equivalent widths. Solar-scaled Kurucz model atmospheres with NEWODF opacities are calculated 
with an independent program. Parameter files control different details, such as the mixing-length parameter and the overshooting. 
FUNDPAR derives the uncertainties following two methods: the criterion of Gonzalez \& Vanture (1998) and the dispersion using the 
$\chi2$ function. The code uses the 2009 version of the MOOG program. The results derived with FUNDPAR are in agreement with previous 
determinations in the literature. The program is freely available from the web\altaffilmark{1}.\medskip}


\resumen{Implementamos un programa en Fortran que determina par\'ametros fundamentales de estrellas de tipo solar, a partir de anchos 
equivalentes del Fe. La soluci\'on debe verificar tres condiciones en el m\'etodo est\'andar: equilibrio de ionizaci\'on, equilibrio de 
excitaci\'on e independencia entre abundancias y anchos equivalentes. Calculamos modelos de atm\'osfera de Kurucz con opacidades NEWODF. 
Detalles como el par\'ametro de longitud de mezcla, el sobre impulso convectivo, etc. se calculan con un programa independiente. FUNDPAR 
calcula las incertezas por dos m\'etodos: el criterio de Gonzalez \& Vanture (1998) y utilizando la funci\'on $\chi^2$. Los resultados 
derivados con FUNDPAR est\'an de acuerdo con determinaciones previas en la literatura. En particular obtuvimos par\'ametros fundamentales 
de 58 estrellas con exoplanetas. El programa est\'a disponible en la red\altaffilmark{1}.}


\addkeyword{stars: abundances}
\addkeyword{stars: fundamental parameters} 


\begin{document}


\maketitle


\section{Introduction}

Different methods have been used in the literature to derive fundamental parameters and metallicities of solar type stars. For instance, 
some studies begin with a photometric estimation of temperature and gravity and then derive the metallicity using equivalent widths. 
Useful codes such as WIDTH9 (Kurucz 1993; Kurucz 1995, private communication) or 
BLACKWEL\footnote[2]{\url{http://www1.appstate.edu/dept/physics/spectrum/spectrum.html}.} (an implementation of the Blackwell method) are 
widely used in the literature \citep[e.g., ][]{saffe-blackwell}. However, the temperature and gravity are usually considered as fixed 
parameters. The observed stellar spectra could be compared with a grid of previously calculated synthetic spectra 
\citep[e.g., ][]{fischer-valenti05,saffe-vega} to determine fundamental parameters. However, in this case the instrumental broadening 
should be taken into account and the rotational velocity could be considered as another independent parameter.

Recently, \citet{sousa10} derived an effective temperature calibration based on line equivalent width ratios of different absorption lines. 
Also, the equivalent widths of Fe lines could be used to determine the parameters of solar type stars. The solution should verify three 
conditions in the standard method: {[FeI/H]$=$[FeII/H]} (i.e., ionization equilibrium), independence between the metallicity and both the 
excitation potential (i.e., excitation equilibrium) and the equivalent widths. This method has been applied to solar type stars, for 
instance, in the determination of metallicity of stars with and without low mass companions or exoplanets (e.g., Gonzalez 1997, 1998; 
Gonzalez, Wallerstein, \& Saar 1999; Santos, Israelian, \& Mayor 2000; Gonzalez \& Laws 2000; Gonzalez et al. 2001; Laws \& Gonzalez 2001; 
Laws et al. 2003). The process estimate initially the fundamental parameters ($T_\mathrm{eff}$, $\log g$, [Fe/H] and $\xi$, the microturbulence 
velocity). This information is used in the ATLAS program (Kurucz 1993; Kurucz 1995, private communication) to derive a model atmosphere 
in LTE (local thermodynamic equilibrium). The model atmosphere with the measured equivalent widths of the spectra, is introduced in the 
code MOOG\footnote[4]{http://verdi.as.utexas.edu/moog.html.} to derive a new metallicity. If the mentioned conditions are not satisfied, the 
process is restarted using new fundamental parameters calculated with the downhill method.

In this contribution, we present the Fortran code FUNDPAR (and their complement {\tt atlas.launcher}) that implements the method explained 
above. The programs are available from the Web\footnote[5]{http://icate-conicet.gob.ar/saffe/fundpar/.}, including detailed installation 
instructions and some technical details such as the format of the input/output files ({\tt install.txt}). As an example of practical use, 
we derived the fundamental parameters of 58 main sequence exoplanet host stars and verified the metal-rich nature of the group. The values 
derived are in agreement with previous determinations from the literature.

In \S~2 we show the general idea and the logic of the program. The procedure of minimization of the $\chi^2$ function is detailed in \S~3. 
The estimation of the uncertainties in the parameters and the comparison with literature, are showed in \S\S~4 and 5, respectively. Finally 
we present some concluding remarks in \S~6.


\section{The logic of the program}

The algorithm is organized in one main procedure and a number of sub-programs with specific tasks. The iterative process begins at one 
starting point in a 4D-space, where the variables are ($T_\mathrm{eff}$, $\log g$, [Fe/H], $\xi$). This starting point could be optionally 
given in the first line of the input file (see the file {\tt install.txt} for details of input/output files). If this point is unknown, 
the program adopts (5000~K, 4.00~dex, $-$0.10~dex, 1.00 km~s$^{-1}$) to begin the iteration. For example, \citet{santos00} estimate 
$T_\mathrm{eff}$ and $\log g$ from the $uvby$ photometry and the calibration of \citet{olsen84}, while [Fe/H] and $\xi$ are estimated 
following \citet{schuster-nissen89} and \citet{edvar93}, respectively.

Then for each iteration step, i.e., for each group of 4 parameters ($T_\mathrm{eff}$, $\log g$, [Fe/H], $\xi$), the program should:
\medskip
\\(a) Generate an appropriate ATLAS model atmosphere (through the {\tt atlas.launcher} program). First, the code should select 
from the Kurucz grid the model atmosphere closest in the parameter space to those requested and take this as initial input model. 
Then the program executes ATLAS9 to derive the final model. 
\medskip
\\(b) Transform the model atmosphere to a format readable by MOOG (subroutine {\tt kurucz2moog}). The format of the model atmosphere 
used by MOOG is not exactly the Kurucz model and should be rewritten accordingly. 
\medskip
\\(c) Call the MOOG program. At this point, the program takes the file containing the equivalent widths of the FeI and FeII lines 
of the star and the model atmosphere as input for the MOOG program. The MOOG program is executed using a driver called ``abfind'' 
which is selected for the abundance determination.
\medskip
\\(d) Read the new metallicity values calculated by MOOG (subroutine {\tt rmr, read-moog-results}); and finally, 
\medskip
\\(e) Determine the value of the $\chi^2$ function. This step will be explained below. \bigskip


%%%%% TABLA 1

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\caption{Sample of the fundpar.par file which\\ contains the weights of the $\chi^2$ function}
\label{fundpar.par}
\begin{tabular}{lcl}
\toprule
t1~=~200.00   &  & \# Characteristic length scale of Teff (K) \\ %$T_\mathrm{eff}$ (K) \\
t2~=~~~~0.10  &  & \# Characteristic length scale of Logg (dex) \\ %$\log g$ (dex) \\
t3~=~~~~0.10  &  & \# Characteristic length scale of [Fe/H] (dex)\\
t4~=~~~~0.10  &  & \# Characteristic length scale of Xita (km~s$^{-1}$) \\ %$\xi$ (km~s$^{-1}$)\\
w1~=~25000.00 &  & \# Chi2 Weight factor \\
w2~=~~2500.00 &  & \# Chi2 Weight factor \\
w3~=~~1111.00 &  & \# Chi2 Weight factor \\
w4~=~~1111.00 &  & \# Chi2 Weight factor \\
\bottomrule
\end{tabular}
\vspace{0.6cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


We take into account the conditions mentioned in the introduction through a variable called $\chi^2$. We adopt for $\chi^2$ the expression 
$\chi^2 = w_{1} c_{1}^2 + w_{2} c_{2}^2 + w_{3} c_{3}^2 + w_{4} c_{4}^2$, where {$w_{1}$,...,$w_{4}$} are weight factors ($w_{i} \ge 0$), $c_{1}$ 
and $c_{2}$ are the slopes in the plots of [Fe/H] vs. {$\log_{10}$(W/$\lambda)$} (logarithm of the reduced equivalent width) and [Fe/H] vs. 
excitation potential, $c_{3}=\mathrm{[FeI/H]-[FeII/H]}$, and $c_{4}$ is the difference between the input ATLAS metallicity (Step a) and the 
resulting metallicity using equivalent widths (Step d). We added explicity the fourth condition: the input metallicity of the model atmosphere 
should be similar to the output metallicity derived from equivalent widths, i.e., the term with $c_{4}$. Then, the four conditions are quantified 
in the $\chi^2$ function: the solution corresponds to the minimum value of $\chi^2$.

The users are free to modify the values of the weights {$w_{1}$,...,$w_{4}$} according to their own criteria. However, we show a simple example 
estimating aproximately the values of the weights. Adopting $\chi^2=1$ as the limiting case of a solution, each condition contributes, for 
example, with 0.25 to the sum {$\chi^2=0.25+...+0.25$}. In this case the 4 conditions are taken equally important within $\chi^2$, 
which is not always true. In the plot of abundance vs. excitation potential, we accept a maximum slope, for instance, of 
{$c_{1}\sim 0.015/4$~dex/eV}, taking a difference of $\sim$0.015~dex in the abundance, for a total range of $\sim$4~eV in the excitation 
potential of Fe lines. Then, in the limiting case, $w_{1} c_{1}^2 \sim 0.25$ and thus $w_{1}\sim 18000$~eV$^2$/dex$^2$. The units of $w_{1}$ 
are forced so as to obtain a dimensionless product $w_{1} c_{1}^2$. In the plot of abundance vs. $\log_{10}$(W/$\lambda$) (where W and 
$\lambda$ are the equivalent width and wavelength in \AA, respectively), we accept a maximum slope (for example) of $c_{2}\sim 0.015/1.5$, 
taking a difference of 0.015~dex in the abundance for a range of $\sim$1.5 in the $\log_{10}$(W/$\lambda$) of Fe lines. Then, 
$w_{2} c_{2}^2 \sim 0.25$ and thus $w_{2}\sim 2500$. For the third condition, $c_{1}=\mathrm{[FeI/H]-[FeII/H]}$ and we adopt a maximum 
difference of 0.015~dex. Then, $w_{3} c_{3}^2 \sim 0.25$ and thus $w_{3} \sim 1100$~dex$^{-2}$. Similarly, for $w_{4}$ result 
$w_{4} \sim 1100$~dex$^{-2}$. In this estimation the weights {$w_{1}$,...,$w_{4}$} turned out to be 18000~eV$^2$/dex$^2$, 2500, 1100~dex$^{-2}$ 
and 1100~dex$^{-2}$, respectively, for a solution in which the four conditions contribute equally with 0.25 to the $\chi^2$ function in the 
limiting case of $\chi^2=1$. In this example those solutions with $\chi^2>1$ do not verify the four conditions.


%%%%%% TABLA 2

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\caption{List of the input and output files used by FUNDPAR}
\label{input.output}
\small
\begin{tabular}{lcccl}
\multicolumn{1}{c}{Filename} &  & Directory &  & \multicolumn{1}{c}{Comment} \\
\toprule
Input Files:\\
\noalign{\smallskip}
{\tt filenames.txt} &  & {\tt datain} &  &  List of files containing the equivalent widths \\
{\tt hd001.txt}     &  & {\tt datain} &  &  Equivalent widths of the star HD 001 \\
...           &  &  ...   &  &  ... \\
{\tt hd999.txt}     &  & {\tt datain} &  &  Equivalent widths of the star HD 999 \\
\midrule
Parameter Files:\\
\noalign{\smallskip}
{\tt atlas.par}     &  & {\tt atlas.launcher} &  & Parameters used by ATLAS \\
{\tt batch.par}     &  & FUNDPAR        &  & Parameters used by MOOG \\
{\tt fundpar.par}   &  & FUNDPAR        &  & Parameters used by FUNDPAR \\
\midrule
Output Files:\\
\noalign{\smallskip}
{\tt hd001.mod}       &  & {\tt dataout} &  & Model atmosphere of HD 001 from ATLAS9\\
{\tt hd001.out1.txt}  &  & {\tt dataout} &  & Output file 1 from MOOG \\
{\tt hd001.out2.txt}  &  & {\tt dataout} &  & Output file 2 from MOOG \\
...             &  & ...     &  & ... \\
{\tt output1.screen}  &  & {\tt dataout} &  & Similar output to the screen\\
{\tt output2.results} &  & {\tt dataout} &  & Table of results for all the stars \\
\bottomrule
\end{tabular}
\vspace{0.4cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


The user will probably have his/her own criteria for the values of {$w_{1}$,...,$w_{4}$}, instead of the values of the example explained 
the previous paragraph. The user is free to modify the values of {$w_{1}$,...,$w_{4}$} (file {\tt fundpar.par}) and this could result in 
more (or less) restrictive conditions. The code uses these values to define $\chi^2$ and then search for the minimum of the function. Then, 
the user should read the values of the slopes and metallicities in the output files to verify if the four conditions are satisfied. The 
values of {$w_{1}$,...,$w_{4}$} previously shown seem to verify in practice the requirements of minimization and verification of the four 
conditions. In Table~\ref{fundpar.par} we show a sample of the file {\tt fundpar.par} where the weights could be modified. Other parameters 
will be explained in the following sections.

According to the definition, $\chi^2$ could be considered as a function that depends on the fundamental parameters 
$\chi^2=\chi^2$($T_\mathrm{eff},~\log g$, [Fe/H], $\xi$). If $\chi^2$ is not a minimum, the algorithm should determine the next set of 
four possible values. These new variables are used in another iteration (following Steps a to e) to derive a new model atmosphere, 
metallicity and, finally, a new value of $\chi^2$. The algorithm that determines the next group of four parameters is called the downhill 
method, and explained in the next section.

In Table~\ref{input.output} we show a list of the input and output files used by FUNDPAR. The format of the input/output files is detailed 
in the file {\tt install.txt}. There are two main directories ({\tt datain} and {\tt dataout}) containing the input and output files of the 
stars. The equivalent widths should be stored in separate files (one file per star), and the names of these files should be listed in 
another file called {\tt filenames.txt}. The files {\tt atlas.par}, {\tt batch.par} and {\tt fundpar.par} contain the values of some 
parameters used in the model calculation and abundance determination and will be explained in the next sections. After the execution of 
FUNDPAR, three output files per star are created: the ATLAS model atmosphere of the solution and two output files directly from the MOOG 
abundance determination. The file {\tt output1.screen} displays similar information on the screen and {\tt output2.results} lists the final 
parameters and their uncertainties.


\section{The downhill simplex method: minimization of $\chi^2$}

In this section we briefly review the minimization procedure for $\chi^2$ as a function of four independent variables, using a Numerical 
Recipes routine called {\tt amoeba} \citep{press92}. The downhill simplex method is due to \citet{nelder-mead65} and requires only function 
evaluations, not derivatives. A simplex could be considered to be a geometrical figure of $N+1$ vertices in $N$-dimensional space (in our 
case, $N=4$). Taking any vertex as the origin, then the four other points define possible vector directions in the 4-dimensional volume.

The downhill simplex method starts with a group of $N+1$, i.e., 5 vertices rather than a single point or vertex. These vertices are displaced 
with a scale length characteristic of the problem. In our case, $\chi^2$ is initially calculated adopting displacements of 200~K, 0.1~dex, 
0.1~dex and 0.1~km~s$^{-1}$ for the variables $T_\mathrm{eff}$, $\log g$, [Fe/H] and $\xi$, respectively. The characteristic lengths could be 
modified in the file {\tt fundpar.par} (see Table~\ref{fundpar.par}). FUNDPAR executes an initial calculation of $\chi^2$ at the vertices 
of the simplex, before the iteration process begins. Then, the downhill method takes a series of steps, usually moving the highest point of 
the simplex, i.e., where $\chi^2$ is maximum. Succesive steps could be visualized as reflections, expansions and contractions of the 4-dimensional 
object. When the simplex finds a valley, it contracts itself down the valley. An appropriate sequence of these steps will converge to the 
minimum of $\chi^2$.

As explained by \citet{press92}, the termination criterion is usually delicate in the minimization process. The program requires that the 
decrease in the function value in the terminating step be fractionally smaller that some tolerance (variable {\tt ftol} within the {\tt amoeba} 
subroutine). The method just described exactly follows \citet{nelder-mead65}. However, in practice we found that for some stars the routine 
converges in a few iteration steps to a solution with $\chi^2 \gg 1$. In such cases the code decreases the tolerance and continues the 
iteration process from the last point. We verified that it is not necessary in this case to restart the process, because the effect of modifying 
the tolerance determines only at which iteration the program stops. We also note that decreasing the tolerance does not guarantee convergence 
of the solution: we are only modifying the termination step or the termination criterion.

With the adopted values of {$w_{1}$,...,$w_{4}$}, the program usually takes less than $\sim$200 iterations to reach a solution. The number of 
iterations is a known problem of the downhill method. If the code reaches a solution with $\chi^2>1$, then the program restarts the iteration 
process using the last solution as a new initial condition. The restart is recomended by \citet{press92} in the downhill method to eliminate 
a probable local minimum of the function. The code restarts the iteration process only once. The user also could manually restart the process 
using the last solution, for instance, as the new initial condition and FUNDPAR will try to reach a solution with a smaller $\chi^2$.


%%%%% TABLA 3

\begin{table}[!t]
\vspace{0.1cm}
\centering
\caption{Parameters adopted in\\ different cases (A,...,E)\\ for 5 sample stars\\ (see text for details)}
\label{combin.pars}
\begin{tabular}{ccccccc}
\toprule
Run &  & ML &  & W &  & D \\
\midrule
A &  & 1.25 &  & 1 &  & 2 \\
B &  & 1.25 &  & 0 &  & 2 \\
C &  & 1.32 &  & 1 &  & 2 \\
D &  & 1.25 &  & 1 &  & 1 \\
E &  & 1.25 &  & 1 &  & 0 \\
\bottomrule
\end{tabular}
\vspace{0.4cm}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\vspace{0.15cm}

\section{Derivation of the model atmospheres} 

Together with the {FUNDPAR} code, we provide another independent program called {\tt atlas.launcher}, which prepares and executes the Kurucz's 
ATLAS9 in LTE. As input of {\tt atlas.launcher} the fundamental parameters $T_\mathrm{eff}$, $\log g$, [Fe/H] and $\xi$ are used. The output is 
an ATLAS solar-scaled model atmosphere corresponding to these parameters. The program uses a parameter file called {\tt atlas.par} that contains 
different parameters used by ATLAS, such as the mixing-length parameter (usually taken as 1.25), and the overshooting weight parameter W, defined 
in Castelli, Gratton, \& Kurucz (1997). A list of files used by ATLAS (grid of precalculated models, Rosseland and ODFs, and a sample of 
{\tt atlas.par}) is presented in the file {\tt install.txt}.


%%%%%% FIGURA 1

\begin{figure*}[!t]
\centerline{\includegraphics[width=0.7\columnwidth]{csaffefig1a.eps}%
\hspace{0.8\columnsep}%
\includegraphics[width=0.7\columnwidth]{csaffefig1b.eps}}
\vspace{0.2cm}
\centerline{\includegraphics[width=0.7\columnwidth]{csaffefig1c.eps}%
\hspace{0.8\columnsep}%
\includegraphics[width=0.7\columnwidth]{csaffefig1d.eps}}
\caption{Difference between the parameters derived in case A and the parameters derived in cases 
B, C, D and E. The differences are plotted vs. $T_\mathrm{eff}$ only for 5 stars. For instance, in 
the $T_\mathrm{eff}$ panel we ploted $\Delta T_\mathrm{eff}=T_\mathrm{eff}\mathrm{(B)}-T_\mathrm{eff}$(A) 
with filled circles. The symbols used in the panels are filled circles (differences B-A), diagonal 
crosses (differences C-A), empty circles (differences D-A) and squares (differences E-A).}
\label{fig.pars}
\vspace{0.62cm}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


Then, the model atmosphere and the equivalent widths are introduced in the MOOG program. We incorporated in this code the solar abundances of 
\citet{grevesse-sauval98} instead of the original from \citet{anders-grevesse89}, except for Fe for which we adopted {[Fe/H]=7.47~dex}. The 
NEWODF opacities use these abundance values \citep{castelli-kurucz03}. MOOG use a parameter file ({\tt batch.par}) where some 
options\footnote[6]{For a complete list of options, see the manual of the MOOG program, \url{http://verdi.as.utexas.edu/moog.html}.} could be 
modified, such as the molecular equilibrium and the van der Waals line damping options.

Literature authors have different preferences for the choice of ATLAS and MOOG parameters. The user is free to modify the parameters according 
to his/her own criteria, and then FUNDPAR will find the corresponding solution. To give an idea of the sensivity of the results, we rederived 
the fundamental parameters of 5 sample stars (HD 106252, HD 177830, HD 190228, HD 195019 and HD 202206) using different combinations of the 
parameters. In the Table~\ref{combin.pars} we show the values of the parameters adopted in different calculations A,...,E. The parameters shown 
are the mixing-length parameter (ML), the overshooting parameter (W) and the line damping option (D). We start the execution of case A adopting 
ML=1.25, W=1 and D=2. In case B we switched off the overshooting, while in case C we adopted a slightly higher ML. In cases D and E we used 
different options for the line damping.

The variation of $T_\mathrm{eff}$, $\log g$, [Fe/H] and $\xi$ (adopting different ML, W and D) is different from star to star. For instance, 
varying W increases the $T_\mathrm{eff}$ for some stars, and decreases it for others. Probably the variation depends on the fundamental 
parameters of the stars. Then, in the Figure~\ref{fig.pars} we show the difference (called $\Delta$) between the parameters derived for 
case A and the parameters derived for cases B, C, D and E. The differences are plotted vs. $T_\mathrm{eff}$ only for the 5 stars previously 
mentioned. All differences are derived with respect to case A. The symbols used in the panels are filled circles (results B-A), diagonal 
crosses (results C-A), empty circles (results D-A) and squares (results E-A). The panels seems to show a slight dependency on $T_\mathrm{eff}$. 
Switching on/off the overshooting (case B), $\Delta T_\mathrm{eff}$, $\Delta \log g$ and $\Delta$[Fe/H] seem to show a dependency on 
$T_\mathrm{eff}$. Increasing ML from 1.25 to 1.32 (case C), we find no clear tendency and the differences are small. Using the damping option 
1 instead of 2 (case D), $T_\mathrm{eff}$, $\log g$ and [Fe/H] increase by an average of $\sim$48~K, $\sim$0.14~dex and $\sim$0.05~dex, 
respectively. Using the damping option 0 (case E), $T_\mathrm{eff}$, $\log g$, [Fe/H] and $\xi$ increase by an average of $\sim$70~K, 
$\sim$0.20~dex, $\sim$0.06~dex and $\sim$0.1~km~s$^{-1}$, respectively. We caution that these preliminary differences have been derived using 
only 5 stars. A larger number of stars is needed to properly determine how the parameters ML, W and D modify the derived fundamental parameters.


%%%%% TABLA 4

\begin{table*}[!t]
\vspace{0.1cm}
\centering
\tablecols{10}
\setlength{\tabnotewidth}{0.82\textwidth}
\setlength{\tabcolsep}{1.2\tabcolsep}
\caption{Fundamental parameters and dispersions derived with FUNDPAR}
\label{tabla.pars}
\footnotesize
\begin{tabular}{lccccccccc}
\toprule
\multicolumn{1}{c}{Star}  & $T_\mathrm{eff}$ & $\log g$ & [Fe/H] & $\xi$ & e$T_\mathrm{eff}$ & e$\log g$ & e[Fe/H] & e$\xi$ & Ref\tabnotemark{1}\\
                          & [K]             & [dex]   & [dex]  & [km~s$^{-1}$] & [K]   & [dex]  &  [dex]  & [km~s$^{-1}$] & \\
\midrule
14 Her           &    5294 &    4.33&    0.50&    0.71&     40.60&    0.19&    0.07&    0.05& R1      \\
16 Cyg A$_1$     &    5704 &    4.29& $-$0.01&    1.32&     90.75&    0.19&    0.11&    0.10& R2      \\
16 Cyg A$_2$     &    5749 &    4.23&    0.07&    1.02&     15.58&    0.04&    0.06&    0.03& R3      \\
16 Cyg B$_1$     &    5632 &    4.36& $-$0.05&    1.21&     83.68&    0.25&    0.10&    0.09& R2      \\
16 Cyg B$_2$     &    5690 &    4.30&    0.05&    0.91&     14.16&    0.04&    0.06&    0.03& R3      \\
47 Uma           &    5720 &    4.26& $-$0.12&    1.31&     86.63&    0.15&    0.10&    0.08& R2      \\
51 Peg$_1$       &    5681 &    4.37&    0.11&    1.21&     62.21&    0.11&    0.08&    0.08& R2      \\
51 Peg$_2$       &    5797 &    4.39&    0.22&    1.13&     16.33&    0.04&    0.04&    0.03& R4      \\
70 Vir           &    5481 &    3.98& $-$0.08&    1.10&     92.16&    0.15&    0.09&    0.07& R2      \\
BD-10 3166       &    5275 &    4.36&    0.32&    0.69&     42.70&    0.05&    0.09&    0.05& R4      \\
HD 106252        &    5844 &    4.50& $-$0.06&    0.98&     12.23&    0.12&    0.05&    0.03& R5      \\
HD 10697         &    5600 &    3.96&    0.10&    1.20&     28.41&    0.03&    0.05&    0.04& R4      \\
HD 108147        &    6279 &    4.59&    0.19&    1.11&     41.51&    0.12&    0.11&    0.09& R5      \\
HD 114783        &    5100 &    4.48&    0.08&    0.87&     15.70&    0.10&    0.07&    0.04& R5      \\
HD 117176        &    5487 &    4.09& $-$0.06&    1.00&     10.86&    0.10&    0.06&    0.02& R5      \\
HD 1237$_1$      &    5537 &    4.50&    0.22&    1.19&     30.76&    0.15&    0.07&    0.05& R4      \\
HD 1237$_2$      &    5468 &    4.50&    0.05&    1.38&     23.27&    0.18&    0.07&    0.04& R6     \\
HD 12661$_1$     &    5670 &    4.41&    0.38&    0.91&     19.18&    0.06&    0.05&    0.03& R4      \\
HD 12661$_2$     &    5719 &    4.48&    0.38&    0.84&     24.28&    0.04&    0.05&    0.04& R4      \\
HD 13445         &    5080 &    4.43& $-$0.30&    0.65&     19.69&    0.23&    0.07&    0.05& R6     \\
HD 134987        &    5719 &    4.28&    0.33&    1.09&     22.44&    0.04&    0.07&    0.04& R4      \\
HD 136118        &    6153 &    4.37& $-$0.09&    2.00&     21.82&    0.15&    0.08&    0.11& R5      \\
HD 141937        &    5832 &    4.50&    0.12&    0.97&     12.63&    0.10&    0.05&    0.03& R5      \\
HD 160691        &    5788 &    4.49&    0.24&    1.12&     22.03&    0.08&    0.06&    0.04& R5      \\
HD 16141$_1$     &    5768 &    4.24&    0.17&    1.10&     22.07&    0.04&    0.04&    0.04& R4      \\
HD 16141$_2$     &    5751 &    4.28&    0.16&    1.00&     12.18&    0.05&    0.05&    0.03& R5      \\
HD 168443        &    5549 &    4.13&    0.08&    1.04&     17.06&    0.02&    0.06&    0.03& R4      \\
HD 168746        &    5566&    4.43&  $-$0.09&    0.94&     10.51&    0.04&    0.05&    0.03& R5      \\
HD 169830$_1$    &    6268&    4.10&    0.20&    1.29&     22.14&    0.18&    0.05&    0.03& R6     \\
HD 169830$_2$    &    6283&    4.23&    0.16&    1.27&     24.27&    0.08&    0.06&    0.06& R5      \\
HD 177830        &    4801&    3.37&    0.38&    0.95&     55.16&    0.07&    0.10&    0.04& R4      \\
HD 187123        &    5792&    4.39&    0.14&    1.04&     26.26&    0.08&    0.04&    0.04& R1      \\
HD 190228        &    5259&    3.64& $-$0.32&    1.13&     11.79&    0.11&    0.05&    0.02& R5      \\
HD 192263        &    4905&    4.38& $-$0.02&    0.73&     19.76&    0.18&    0.08&    0.05& R4      \\
HD 195019a       &    5731&    4.17&    0.00&    1.20&     13.09&    0.13&    0.05&    0.03& R5      \\
HD 19994.2       &    6147&    4.35&    0.12&    2.03&     23.94&    0.10&    0.08&    0.09& R5      \\
HD 202206$_1$    &    5635&    4.55&    0.28&    0.88&     24.27&    0.14&    0.06&    0.04& R6     \\
HD 202206$_2$    &    5713&    4.45&    0.30&    1.07&     14.42&    0.04&    0.06&    0.03& R5      \\
HD 209458        &    6065&    4.43&    0.02&    1.14&     18.56&    0.13&    0.06&    0.04& R4      \\
HD 210277        &    5517&    4.34&    0.24&    0.84&     26.56&    0.12&    0.05&    0.04& R1      \\
HD 217107        &    5602&    4.42&    0.42&    0.87&     17.64&    0.03&    0.05&    0.03& R4      \\
HD 22049         &    5083&    4.47& $-$0.14&    0.84&     14.29&    0.15&    0.06&    0.04& R5      \\
HD 222582        &    5719&    4.25&    0.00&    0.99&     18.90&    0.03&    0.04&    0.04& R4      \\
HD 27442         &    4859&    3.60&    0.38&    1.21&     45.85&    0.22&    0.15&    0.06& R5      \\
HD 28185         &    5637&    4.54&    0.21&    0.96&     13.79&    0.04&    0.06&    0.03& R5      \\
HD 33636         &    5877&    4.27& $-$0.13&    0.95&     14.81&    0.10&    0.06&    0.04& R5      \\
HD 37124$_1$     &    5579&    4.60& $-$0.39&    0.74&     19.83&    0.11&    0.09&    0.08& R5      \\
HD 37124$_2$     &    5495&    4.46& $-$0.42&    0.71&     22.54&    0.04&    0.05&    0.07& R4      \\
HD 38529         &    5600&    3.82&    0.34&    1.25&     38.21&    0.05&    0.06&    0.03& R4      \\
HD 4203          &    5667&    4.43&    0.43&    1.08&     29.95&    0.06&    0.15&    0.06& R5      \\
HD 4208          &    5592&    4.33& $-$0.29&    0.87&     14.74&    0.15&    0.06&    0.04& R5      \\
\bottomrule
\end{tabular}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%% TABLA 4 CONT

\setcounter{table}{3}
\begin{table*}[!t]
\vspace{0.1cm}
\centering
\centerline{TABLE~4 (CONTINUED)\smallskip}
\setlength{\tabnotewidth}{0.8\textwidth}
\tablecols{10}
\setlength{\tabcolsep}{1.2\tabcolsep}
\footnotesize
\begin{tabular}{lccccccccc}
\toprule
\multicolumn{1}{c}{Star}  & $T_\mathrm{eff}$ & $\log g$ & [Fe/H] & $\xi$ & e$T_\mathrm{eff}$ & e$\log g$ & e[Fe/H] & e$\xi$ & Ref\tabnotemark{1}\\
                          & [K]             & [dex]   & [dex]  & [km~s$^{-1}$] & [K]   & [dex]  &  [dex]  & [km~s$^{-1}$] & \\
\midrule
HD 46375$_1$     &    5210&    4.37&    0.24&    0.65&     35.26&    0.10&    0.06&    0.04& R4      \\
HD 46375$_2$     &    5252&    4.50&    0.26&    0.68&     21.15&    0.09&    0.10&    0.06& R5      \\
HD 50554         &    5978&    4.51& $-$0.01&    1.10&     11.93&    0.10&    0.06&    0.03& R5      \\
HD 52265$_1$     &    6102&    4.28&    0.24&    1.20&     17.71&    0.06&    0.05&    0.03& R4      \\
HD 52265$_2$     &    6163&    4.37&    0.27&    1.21&     19.51&    0.10&    0.03&    0.03& R4      \\
HD 52265$_3$     &    5993&    4.21&    0.17&    1.24&     25.17&    0.18&    0.06&    0.04& R6     \\
HD 6434          &    5715&    4.32& $-$0.54&    0.70&     23.11&    0.16&    0.11&    0.10& R5      \\
HD 68988         &    5936&    4.49&    0.32&    1.19&     19.40&    0.02&    0.09&    0.05& R5      \\
HD 75289$_1$     &    6138&    4.52&    0.27&    1.50&     20.96&    0.10&    0.07&    0.05& R7     \\
HD 75289$_2$     &    6070&    4.44&    0.23&    1.42&     30.93&    0.16&    0.06&    0.05& R6     \\
HD 75332         &    6277&    4.47&    0.22&    1.03&     24.73&    0.11&    0.05&    0.04& R4      \\
HD 82943$_1$     &    5950&    4.45&    0.28&    1.10&     25.37&    0.07&    0.05&    0.03& R6     \\
HD 82943$_2$     &    5987&    4.46&    0.24&    1.11&     17.85&    0.04&    0.05&    0.03& R5      \\
HD 83443$_1$     &    5389&    4.31&    0.33&    1.00&     27.40&    0.18&    0.08&    0.04& R6     \\
HD 83443$_2$     &    5427&    4.40&    0.34&    0.99&     22.07&    0.13&    0.07&    0.05& R5      \\
HD 8574          &    6029&    4.34&    0.00&    1.19&     13.29&    0.16&    0.05&    0.03& R5      \\
HD 89744         &    6315&    4.16&    0.27&    1.67&     28.06&    0.07&    0.04&    0.05& R4      \\
HD 92788         &    5755&    4.43&    0.29&    1.02&     26.37&    0.04&    0.05&    0.04& R4      \\
HD 95128         &    5832&    4.31&    0.02&    1.08&     13.83&    0.10&    0.05&    0.02& R5      \\
HR 810           &    6072&    4.48&    0.15&    1.23&     27.89&    0.09&    0.07&    0.08& R4      \\
$\nu$ And$_1$    &    6165&    4.21&    0.13&    1.40&     50.44&    0.03&    0.06&    0.07& R8     \\
$\nu$ And$_2$    &    6150&    4.14&    0.09&    1.48&     50.48&    0.03&    0.07&    0.07& R7     \\
$\rho$ Cnc$_1$   &    5201&    4.27&    0.32&    0.78&     99.87&    0.20&    0.11&    0.10& R2      \\
$\rho$ Cnc$_2$   &    5206&    4.40&    0.41&    0.69&     27.42&    0.18&    0.07&    0.04& R7     \\
$\rho$ Crb       &    5751&    4.15& $-$0.24&    1.33&     28.85&    0.05&    0.04&    0.05& R2      \\
$\tau$ Boo$_1$   &    6517&    4.37&    0.30&    1.57&     60.99&    0.04&    0.06&    0.08& R8     \\
$\tau$ Boo$_2$   &    6415&    4.23&    0.30&    1.34&     49.61&    0.06&    0.08&    0.07& R7     \\
\bottomrule
\noalign{\smallskip}
\tabnotetext{1}{References for the equivalent widths (last column): R1: \citet{gonzalez99}, R2: \citet{gonzalez98}, R3: \citet{laws-gonzalez01}, 
R4: \citet{gonzalez01}, R5: \citet{laws03}, R6: \citet{santos00}, R7: \citet{gonzalez-laws00}, R8: \citet{gonzalez97}.}
\end{tabular}
\vspace{0.82cm}
\end{table*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\section{Uncertainty estimation of the derived parameters}

The uncertainties in the atmospheric parameters were estimated following \citet{gonzalez-vanture98}. The uncertainty in 
$\xi$ was determined from the standard deviation of the slope of the least-squares fit of abundance vs. reduced equivalent 
width. Then, the dispersion of the effective temperature was determined from the uncertainty of the slope of the least-squares 
fit of abundance vs. excitation potential, in addition to the uncertainty of the slope due to the uncertainty of $\xi$. 
The uncertainty of the Fe abundance was derived combining the uncertainties of $T_\mathrm{eff}$, $\xi$ and the scatter of 
the individual FeI abundances (standard deviation of the mean), all added in quadrature. In calculating the uncertainty 
of $\log g$, we include the contribution from the uncertainty of $T_\mathrm{eff}$ in addition to the scatter in the FeII 
line abundances.

We derive another estimation of the uncertainty of the solution using $\chi^2$. As we explained previously, we select the 
values of the weights such that solutions with $\chi^2>1$ do not verify the four conditions. Then, we adopt the size of the region 
$\chi^2=1$ as another estimation of the uncertainty of the solution. FUNDPAR stores a record of the points with $\chi^2<1$ 
and uses them to estimate the size of the region. The range of the values of $T_\mathrm{eff}$, $\log g$, [Fe/H] and $\xi$ is 
shown in the results along with the number $n$ of solutions with $\chi^2<1$. These dispersion values should be taken with caution 
if $n$ is small. This kind of uncertainty is comparable to those derived by the criteria of \citet{gonzalez-vanture98}. In the 
next section we present a histogram comparing both uncertainties for a group of exoplanet host stars. The user is free to select 
among them, or to take the maximum value, for instance.

\vspace{0.2cm}

FUNDPAR include the uncertainty estimation of the parameters and they are shown in the ouput files. The size of the uncertainty 
depends on many factors, such as the number of lines involved (which is usually small for FeII), the measured equivalent widths and 
the laboratory data of the spectral lines. The $\log gf$ values (oscillator strength) and excitation potential of the lines are 
important because many derived values (Fe abundances, the slopes of abundance vs. equivalent widths and vs. excitation potential, 
etc.) depend on these quantities. We note that the inclusion of a line which (for one reason or another) implies an abundance very 
different from the average could modify the results and/or increase the uncertainty of the parameters. These lines should be 
eliminated from the list of measured equivalent widths. The abundances of individual lines are shown in the file {\tt out2.txt} 
({\tt work.dir} directory).


\section{Comparison with literature values}

There are small differences in the parameters derived using this method by different authors. \citet{santos00} derived surface 
gravities systematically larger than the ones obtained by other authors \citep[e.g., ][]{gonzalez01} by 0.15~dex. To solve this 
problem, Santos, Israelian, \& Mayor (2004) adopted new $\log gf$ values for the iron lines. Then the authors found a small 
average difference of +25~K in the temperature compared to the studies of \citet{gonzalez01} and \citet{laws03} (57 stars in common). 
Also their $\log g$ are +0.05~dex (on average) larger and the average differences in metallicity are between $-$0.10 and +0.10~dex. 
\citet{ammler09} derived the fundamental parameters of host stars with transiting planets using the 2002 version of the code 
MOOG and ATLAS model atmospheres. However, for the TrES and HAT objects the abundances determined by \citet{sozzetti07} and 
\citet{sozzetti09} using essentially the same method are systematically lower ($\sim$0.10~dex) than those derived by Ammler-von Eiff 
et al. (2009). The authors also mention differences in temperature ($\sim$100~K) and gravity ($\sim$0.15~dex) due to possible systematic 
differences between the works, and they note that the origin of the abundance discrepancies is usually unidentified.


%%%%% FIGURA 2

\begin{figure}[!t]
\centerline{\includegraphics[clip,width=0.99\columnwidth]{csaffefig2a.eps}}
\vspace{0.3cm}
\centerline{\includegraphics[clip,width=0.99\columnwidth]{csaffefig2b.eps}}
\caption{Plots of abundance vs. excitation potential and abundance vs. {$\log_{10}(W/\lambda)$} 
(logarithm of the reduced equivalent width) for HD 106252.}
\label{fig2}
\vspace{0.3cm}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


We compare the parameters derived using {FUNDPAR} and those from the literature 
\citep{gonzalez97,gonzalez98,gonzalez99,santos00,gonzalez-laws00,gonzalez01,laws-gonzalez01,laws03}. We select these works 
in particular because they present the Fe equivalent widths: we use the same values with FUNDPAR. In the Table~\ref{tabla.pars} 
we show the $T_\mathrm{eff}$, $\log g$, [FeI/H] and $\xi$ obtained. Some stars in the table are listed twice (they are identified 
with a subscript) because we have different equivalent width sources in the literature. The sources of the equivalent widths 
are listed in the Table~\ref{tabla.pars} as R1,...,R8.

We show in Figure~\ref{fig2} an example of plots of abundance vs. excitation potential and abundance vs. {$\log_{10}(W/\lambda)$} 
(logarithm of the reduced equivalent width) for HD 106252. In Figure~\ref{fig1} we present the difference between FUNDPAR parameters 
and literature values ($y$ axis, $\Delta$=FUNDPAR-literature) vs. literature values ($x$ axis). The empty point in Figure~\ref{fig1} 
corresponds to the star HD 38529, and shows that the slopes, metallicities and $\chi^2$ values for this object should be taken with 
caution. The derived parameters of this star are based only on 3 FeII lines (and 24 FeI lines). In the literature, some values of 
$T_\mathrm{eff}$, $\log g$ and $\xi$ have been rounded to within 50~K or 10~K, 0.05~dex and 0.1~km~s$^{-1}$, respectively 
\citep[see, for example,][]{gonzalez97,gonzalez98,gonzalez99}. There is a good agreement between {FUNDPAR} parameters and previous 
values from the literature, within the errors, which is expected since {FUNDPAR} uses a very similar method. However, Figure~3 shows 
that there is a dispersion in the values of the parameters (particularly $\log g$ and $\xi$) and probably a systematic trend for the 
metallicity ($\sim$0.01~dex below literature values, see next discussion). The values of $\Delta T_\mathrm{eff}$ and $\Delta \log g$ 
also seem to slightly decrease with $T_\mathrm{eff}$ and $\log g$, respectively. The medians of the differences for the fundamental 
parameters compared to literature values are 24~K, 0.06~dex, 0.03~dex and 0.08~km~s$^{-1}$, corresponding to $T_\mathrm{eff}$, $\log g$, 
[Fe/H] and $\xi$, respectively. The largest differences in the parameters amount to 118~K (16 Cyg B), 0.30~dex (HD 27442), 0.16~dex 
(16 Cyg B) and 0.31~km~s$^{-1}$ (47 Uma), corresponding to $T_\mathrm{eff}$, $\log g$, [Fe/H] and $\xi$, respectively.


%%%% FIGURA 3

\begin{figure*}[!t]
\centerline{\includegraphics[width=0.7\columnwidth]{csaffefig3a.eps}%
\hspace{0.8\columnsep}%
\includegraphics[width=0.7\columnwidth]{csaffefig3b.eps}}
\vspace{0.3cm}
\centerline{\includegraphics[width=0.7\columnwidth]{csaffefig3c.eps}%
\hspace{0.8\columnsep}%
\includegraphics[width=0.7\columnwidth]{csaffefig3d.eps}}
\caption{Difference between FUNDPAR parameters and literature ($y$ axis) vs. literature ($x$ axis). 
The panels shows separately the effective temperature, gravity, metallicity and $\xi$. Filled and 
empty points correspond to solutions with {$\chi^2<1$} and {$\chi^2>1$}, respectively.}
\label{fig1}
\vspace{0.5cm}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


Now we discuss the possible origin of the dispersions and probable trends observed in Figure~\ref{fig1}. We tested FUNDPAR 
significantly modifying the values of the weights {$w_{1}$,...,$w_{4}$} in the function $\chi^2$ and verified that the difference 
in [Fe/H] compared with literature values and the dispersion of the other parameters change very slightly. Then the weights 
{$w_{1}$,...,$w_{4}$} do not seem to be the cause. We use a method similar to that of the literature; however it is not totally 
identical. FUNDPAR uses Kurucz model atmospheres \citep{castelli-kurucz03} different from those used in the literature (most of 
them date from before the creation of the ODFNEW models). The code uses model atmospheres derived by ATLAS with ODFNEW opacities 
and solar abundances from \citet{grevesse-sauval98} instead of \citet{anders-grevesse89}. The new models present differences 
compared to older Kurucz models \citep{kurucz90}, such as the solar abundances, the replacement of TiO and H$_2$0 molecular 
lines, some HI quasi-molecular absorptions, etc. which are taken into account in the NEWODF opacities. Preliminary improvements 
are the $U-B$ and $u-b$ color indices for $T_\mathrm{eff} < 6750$~K, all color indices for cooler stars, and the better modeling 
for the upper layers of cool and giant stars \citep{castelli-kurucz03}. In this example, the model atmospheres are computed 
with convection (mixing-lenght parameter$=$1.25), overshooting (W=1) and damping in the Uns\"old approximation, but multiplied 
by a factor as suggested by Blackwell, Lynas-Gray, \& Smith (1995). The use of the fourth condition within the function $\chi^2$ 
is (possibly) another difference from previous studies. Literature works surely take this into account, but it is not totally 
clear for us how they do so. Finally, we use the MOOG 2009 version\footnote[7]{\url{http://verdi.as.utexas.edu/moog.html}.} of 
the program instead of the 2002 version used in the literature, although we expect almost the same abundance values from both versions.

These differences, at least in part, produce the slightly dissimilar values showed in the Figure~\ref{fig1}, which suggest 
that FUNDPAR probably uses a different metallicity scale than that of the literature. A complete comparison requires the exact 
knowledge of all involved details used in the literature calculations. Our intention is to clearly present all the asumptions 
used in FUNDPAR, in the model atmospheres and within the code.

In Figure~\ref{histog.uncer} we show the histogram distributions of the uncertainties derived for $T_\mathrm{eff}$, $\log g$, 
[Fe/H] and $\xi$. The densely and slightly shaded histograms correspond to uncertaities derived following \citet{gonzalez-vanture98} 
and using the $\chi^2$ function, respectively. Some distributions present a peak in a common uncertainty value, such as 
$\sim$0.05~dex in the [Fe/H] distribution and $\sim$30~K in the distribution of effective temperature. We see that the 
errors derived using both methods are comparable.


%%%%% FIGURA 4

\begin{figure*}[!t]
\centerline{\includegraphics[width=6cm,height=6.18cm]{csaffefig4a.eps}%
\hspace{0.8\columnsep}%
\includegraphics[width=6cm]{csaffefig4b.eps}}
\vspace{0.3cm}
\centerline{\includegraphics[width=6cm,height=6.18cm]{csaffefig4c.eps}%
\hspace{0.8\columnsep}%
\includegraphics[width=6cm]{csaffefig4d.eps}}
\caption{Histogram distributions of the uncertainties in $T_\mathrm{eff}$, $\log g$, [Fe/H] and 
$\xi$ derived with FUNDPAR. The densely and slightly shaded histograms correspond to uncertaities 
derived following \citet{gonzalez-vanture98} and using the $\chi^2$ function, respectively.}
\label{histog.uncer}
\vspace{0.5cm}
\end{figure*}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


The metallicities presented in Table~\ref{tabla.pars} correspond to a group of exoplanet host stars. The median of the group is 0.17~dex 
with a dispersion of 0.22~dex. In Figure~\ref{histog.feh} we present the histogram of the metallicity distribution. Then, as an example 
of the practical use of {FUNDPAR}, we verified the metal-rich nature of main sequence stars with low mass companions, a fact known from 
the literature \citep[see, for example,][]{gonzalez97,santos00}.


%%%%% FIGURA 5

\begin{figure}[!t]
\vspace{0.1cm}
\centering
\includegraphics[width=0.99\columnwidth]{csaffefig5.eps}
\caption{Metallicity distribution of the sample stars derived by FUNDPAR.}
\label{histog.feh}
\vspace{0.7cm}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\vspace{0.2cm}

\section{Concluding remarks}

We have implemented a Fortran algorithm available from the web that estimates fundamental parameters of solar type stars, requiring 
only the measurement of Fe equivalent widths. The final solution should verify the three conditions of the standard method: 
{[FeI/H]$=$[FeII/H]} (i.e., ionization equilibrium), independence of the metallicity from the excitation potential (i.e., excitation 
equilibrium) and from the equivalent widths. We also add another condition: the input metallicity used in the model atmosphere 
should be similar to the resulting metallicity from the equivalent widths. We taken into account these conditions in one variable 
called $\chi^2$, adopting an expression which includes the weights {$w_{1}$,...,$w_{4}$}. FUNDPAR uses Kurucz model atmospheres with 
the NEWODF opacities \citep{castelli-kurucz03}, solar-scaled abundances from \citet{grevesse-sauval98} and the 2009 version of the 
MOOG program. Different details could be selected, such as the mixing-lenght parameter, the overshooting and the damping of the lines, 
for instance. We have planed a new version that includes the option of using the WIDTH9 program instead of MOOG.

The code includes the derivation of the uncertainty in the four parameters following the criteria of Gonzalez \& Vanture (1998) and 
another uncertainty estimation using the $\chi^2$ function. We verified the metal-rich nature of a group of exoplanet host stars. 
The parameters derived with FUNDPAR are in agreement with previous values in the literature.

%\vspace{0.45cm}

\acknowledgements

The author thank R.~L. Kurucz, C. Sneden, L. Sbordone, P. Bonifacio and F. Castelli for making their codes available to him. 
We also thank the anonymous referee whose suggestions improved the paper. This work was partially supported by a grant PIP 1153 
from Consejo Nacional de Investigaciones Cient\'ificas y T\'ecnicas de la Rep\'ublica Argentina.


\vspace{0.35cm}

\begin{thebibliography}

\vspace{0.1cm}

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\bibitem[Anders \& Grevesse(1989)]{anders-grevesse89} Anders, E., \& Grevesse, N. 1989, Geochim. Cosmochim. Acta, 53, 197

\bibitem[Blackwell et al.(1995)]{blackwell95} Blackwell, D.~E., Lynas-Gray, A., \& Smith, G. 1995, A\&A, 296, 217

\bibitem[Castelli et al.(1997)]{castelli97} Castelli, F., Gratton, R., \& Kurucz, R. 1997, A\&A, 318, 841

\adjustfinalcols

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