\begin{table}%t6
\caption{\label{table:comparison}Comparison of the deduced fractional abundances to other observational studies and theoretical predictions.}
\par
%\centering
\par
 {
\begin{tabular}{lccccccccc}
\hline \hline \noalign{\smallskip}
& $^{12}$CO & $^{13}$CO & CS & HCN & CN & SiO & SiS & SO & SO$_2$ \\
\hline \noalign{\smallskip}
\citet{Lindqvist1988AandA...205L..15L}\tablefootmark{a} & $1.5 \times 10^{-4}$ & $-$ & $1.5 \times 10^{-7}$ & $3.0 \times 10^{-7}$  & $-$ & $-$ & $3.5 \times 10^{-7}$ & $-$ &$-$ \\
\citet{Omont1993AandA...267..490O}\tablefootmark{b} & $-$& $-$ & $-$ & $-$ &  $-$ &$1.5 \times 10^{-6}$ & $-$ & $9 \times 10^{-7}$ & $2.05 \times 10^{-6}$ \\
\citet{Bujrrabal1994AandA...285..247B}\tablefootmark{c} & $1.5 \times 10^{-4}$ & $1.6 \times 10^{-5}$ & $5.0 \times 10^{-8}$ & $4.9 \times 10^{-7}$  &  $-$ & $8.5 \times 10^{-6}$ & $2.2 \times 10^{-7}$ & $1.3 \times 10^{-6}$ & $-$ \\
\citet{Kim2009}\tablefootmark{d} (``case A'') & $1.5 \times 10^{-4}$ & $1.75 \times 10^{-5}$ & $3.0 \times 10^{-7}$ & $1.4 \times 10^{-6}$ &   $1.6 \times 10^{-7}$& $1.3 \times 10^{-5}$ & $1.3 \times 10^{-6}$ & $7.8 \times 10^{-7}$ & $1.4 \times 10^{-5}$ \\
 \citet{Kim2009}\tablefootmark{d} (``case B'') &$1.5 \times 10^{-4}$ & $1.75 \times 10^{-5}$ & $8.1 \times 10^{-8}$ & $4.3 \times 10^{-7}$ &  $5.1 \times 10^{-8}$ & $5.1 \times 10^{-6}$ & $3.1 \times 10^{-7}$ & $2.7 \times 10^{-7}$ & $4.2 \times 10^{-6}$ \\
\hline \noalign{\smallskip}
Gonz\'alez Delgado\tablefootmark{e}  &  &  & &  &   & & &  &  \\
et~al. (2003) & {\raisebox{1.5ex}[0pt]{$1.0 \times 10^{-4}$}} &{\raisebox{1.5ex}[0pt]{$-$}}  & {\raisebox{1.5ex}[0pt]{$-$}} &{\raisebox{1.5ex}[0pt]{$-$}}  &  {\raisebox{1.5ex}[0pt]{$-$}} & {\raisebox{1.5ex}[0pt]{$2.0 \times 10^{-7}$}} & {\raisebox{1.5ex}[0pt]{$-$}} & {\raisebox{1.5ex}[0pt]{$-$}} & {\raisebox{1.5ex}[0pt]{$-$}}  \\
\citet{Schoier2007AandA...473..871S}\tablefootmark{f} & $1.0 \times 10^{-4}$ & $-$ &$-$  &$-$  &  $-$ &  $-$ & $5 \times 10^{-6}$& $-$ & $-$\\
 & & & & & & & -- $5.0 \times 10^{-9}$ & &  \\
this work& $1.0 \times 10^{-4}$ & $7.1 \times 10^{-6}$ & $4 \times 10^{-8}$ & $2.2 \times 10^{-7}$ &  $1.0 \times 10^{-10}$  & $8.0 \times 10^{-6}$ & $5.5 \times 10^{-6}$ & $2.0 \times 10^{-7}$ & $1.0 \times 10^{-6}$ \\
 & & & & & -- $3.0\times 10^{-8}$  & -- $2.0 \times 10^{-7}$ &--  $4.0 \times 10^{-9}$&  & \\
\hline \noalign{\smallskip}
\citet{Duari1999AandA...341L..47D}\tablefootmark{h} & $5.38 \times 10^{-4}$ & $-$ & $2.75 \times 10^{-7}$ & $2.12 \times 10^{-6}$ & $2.40 \times 10^{-10}$ & $3.75 \times 10^{-5}$ & $3.82 \times 10^{-10}$ & $7.79 \times 10^{-8}$ & $-$\\
\citet{Cherchneff2006AandA...456.1001C}\tablefootmark{i} & $6.71 \times 10^{-4}$ & $-$ & $1.85 \times 10^{-5}$ & $9.06 \times 10^{-5}$ & $3 \times 10^{-11}$$^g$ & $4.80 \times 10^{-5}$ & $7 \times 10^{-8}$ & $1 \times 10^{-7}$ &  $1 \times 10^{-12}$ \\
\citet{Willacy1997AandA...324..237W}\tablefootmark{j} & $4 \times 10^{-4}$ & $-$ & $2.9 \times 10^{-7}$ & $1.4 \times 10^{-7}$ & $3.5 \times 10^{-7}$ & $3.2 \times 10^{-5}$ & $3.5 \times 10^{-6}$ & $9.1 \times 10^{-7}$ & $2.2 \times 10^{-7}$\\
\hline
\end{tabular}}
\tablefoot {In the first part of the table, observational results are listed based on the assumption of optically thin emission and a population distribution which is thermalized at one excitation temperature.  The second part gives observational results based on a non-LTE radiative transfer analysis. Theoretical predictions for either the inner envelope \citep{Duari1999AandA...341L..47D, Cherchneff2006AandA...456.1001C} or outer envelope \citep{Willacy1997AandA...324..237W} fractional abundances are given in the last part.\\
All fractional abundances are given relative to the total H-content. In cases where values found in literature were given relative to H$_2$, they were re-scaled relative to the total H-content by assuming that all hydrogen is in its molecular form H$_2$.}
\tablebib {\tablefoottext{a}{No information on used distance and mass-loss rate;}
\tablefoottext{b}{distance is 270~pc, \Mdot~= $4.5$~$\times$ $10^{-6}$~\Msun/yr;}
\tablefoottext{c}{distance is 270~pc, \Mdot~= $4.5$~$\times$ $10^{-6}$~\Msun/yr;}
\tablefoottext{d}{distance is 250~pc, assumed \Mdot\ of $4.7$~$\times$ $10^{-6}$~\Msun/yr, LTE is assumed, ``case~B'' represents a solution with a larger outer radius than ``case~A'';}
\tablefoottext{e}{$r_{\rm e}$ in Gaussian distribution for SiO is $2.5$~$\times$ $10^{16}$~cm, distance is 250~pc and \Mdot~= $3$~$\times$ $10^{-5}$~\Msun/yr;}
\tablefoottext{f}{$r_{\rm e}$  in Gaussian distribution for SiS, distance is 260~pc and \Mdot~= $1$~$\times$ $10^{-5}$~\Msun/yr. For 2-component model: $f_{\rm c}$~is $5.5$~$\times$ $10^{-6}$ and taken constant out to $1.0$~$\times$ $10^{15}$~cm and  the lower abundance Gaussian component has~$f_0$ of $5.0$~$\times$ $10^{-9}$ and~$r_{\rm e}$ of $1.6$~$\times$ $10^{16}$~cm. Using one (Gaussian) component distribution, $f_0$~is $5$~$\times$ $10^{-8}$ and $r_{\rm e}$ is $1.6$~$\times$ $10^{16}$~cm;}
\tablefoottext{g}{only value at  5~\Rstar\ is given;}
\tablefoottext{h}{predicted values at 2.2~\Rstar\ in the envelope for IK~Tau;}
\tablefoottext{i}{predicted values at 2~\Rstar\ in the envelope for TX~Cam;}
\tablefoottext{j}{predicted peak fractional abundances in the outer envelope.}}
\vspace*{5mm}
\end{table}