\begin{table}%T1
  \caption{PDR models of the Horsehead nebula.}
  \label{tab_mod}
  %\centerline
{
    \begin{tabular}{lrrrrrrrrrr}
     \hline\hline
        {\bf Constant density models}\\
	$Model$ & $n_{\rm H}$\ \ \  & $G_0$ & $A_{\rm V}$
	& CO\ ~ & CO\ ~  & CO\ ~ &
	\thco & \ceio & \ci\ \ ~ & $\chi^2$
	\\
	& & & & (2$-$1) & (4$-$3) & (6--5) &
	(2$-$1) & (2$-$1) & (1--0) &
	\\
       \hline %\\[-5pt]
	Pos A & & & & 40.5 & 24.8 & 12.0 & 15.2 &  7.3 & 11.1 \\
	A1 $\ast$  & $5   \times 10^4$ & 25  & 36
	&             43.2 & 29.7 &  8.9 & 14.9 &  7.8 & 11.6 & 0.27 \\  %H457
	A2  & $3   \times 10^4$ & 25  & 36
	&             38.9 & 23.8 &  5.1 & 14.7 &  8.1 & 11.7 & 1.11 \\  %H458
	A3  & $7   \times 10^4$ & 25  & 36
	&             46.2 & 33.8 & 12.5 & 14.9 &  7.5 & 11.4 & 0.88 \\  %H452
	A4  & $5   \times 10^4$ & 55  & 36
	&             45.2 & 31.8 & 10.4 & 16.2 &  8.4 & 12.9 & 0.61 \\  %H459
	A5  & $5   \times 10^4$ & 10  & 36
	&             41.5 & 27.9 &  7.7 & 13.5 &  7.0 & 10.1 & 0.39 \\  %H460
	A6  & $5   \times 10^4$ & 25  & 26
	&             42.7 & 29.3 &  8.7 & 14.0 &  6.3 & 11.6 & 0.33 \\  %H461
        \hline %\\[-5pt]
	Pos B & & & & 32.5 & 18.2 & --  &  9.5 & 0.78 &  5.1 \\
	B1 $\ast$  & $3 \times 10^4$ &  1 & 6
	&             30.9 & 17.2 &  2.0 &  8.0 & 0.92 &  5.4 & 0.32 \\  %H465
	B2  & $3 \times 10^4$ &  2 & 6
	&             32.7 & 19.0 &  2.6 &  8.1 & 0.56 &  7.1 & 1.29 \\  %H463
        \hline %\\[-5pt]
	Pos C & & & & 40.2 & 25.0 & -- & 9.20 &  0.89 &  8.5 \\
	C1 $\ast$  & $5 \times 10^4$ &  7 & 8
	&             38.8 & 26.5 &  7.1 &  9.5 & 0.93 &  9.2 & 0.12 \\  %H470
        \hline %\\[-5pt]
	Pos D & & & & 51.7 & 37.8 & 22.7 & 13.8 &  6.0 &  7.4 \\
	D1 $\ast$ & $7  \times 10^4$ & Star  & 22
	&             54.7 & 42.9 & 19.6 & 16.1 &  5.9 &  8.0 & 0.32 \\  %H472
	\hline
	{\bf Isobaric models}\\
	$Model$ & $p$\ \ \  & $G_0$ & $A_{\rm V}$ & CO\ ~ & CO\ ~  & CO\ ~ &  \thco & \ceio & \ci\ \ ~ & $\chi^2$ \\
	& & & & (2$-$1) & (4$-$3) & (6--5) & (2$-$1) & (2$-$1) & (1--0) & \\
       \hline %\\[-5pt]
        D2 &	$4 \times 10^6$ & Star & 22 & 60.0& 51.1 & 29.2 & 15.7 & 5.7 & 6.23 & 1.16 \\
        D3 & $2\times 10^6$ &          &    & 54.0 & 42.5 & 20.7 & 15.6 & 5.7 & 6.6 & 0.23 \\
        D4 & $1\times 10^6$ & 	       &    & 48.4 & 34.7 & 13.7 & 15.4 & 5.8 & 7.2 & 0.77 \\
      \hline
      \end{tabular}}
\medskip
  N{\sc otes:} Entries in the table are: Model number, computed
  intensities of the CO~(2$-$1), (4$-$3), (6--5), \thco~(2$-$1),
  \ceio~(2$-$1), and \ci~(1--0) emission (K~km~s$^{-1}$), as well as the
  $\chi^2$ value of the fit. The observed line intensities for
  positions A--C that are used in the fit are also given (we
  estimate the calibration uncertainty to be $\sim$20\%). Best-fit
  models are marked with an asterisk. The radiation field $G_0$
  (Pos \emph{A} -- \emph{C})
%is characterized by the Draine field, in
%  units of the Draine field, $2.7 \times 10^{-3}$ erg/s/cm$^2$
    in Draine units. The
  neck is illuminated double-sided with $G_0$ from the front
  $\underline {and}$ back side.
\end{table}