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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f01.eps}}\end{figure}$ Figure 1: The photoionization cross sections for the elemental abundances given in Table A.1. The cross section for Compton scattering is calculated for hydrogen.
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f02.eps}}\end{figure}$ Figure 2: Physical and thermal structure of AFGL 2591. The power-law density distribution is adopted from the model of van der Tak et al. (1999). The gas temperature profile was calculated by Doty et al. (2002).
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f03.eps}}\end{figure}$ Figure 3: Ionization rates $\zeta _{{\rm H_2}}$ for the X-ray models presented in Table 1 and a constant cosmic-ray ionization rate $\zeta _{{\rm cr}} = 5.6 \times 10^{-17}$ s^-1. The arrow indicates the distance out to which an inner UV field is effective.
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In the text

$\begin{figure} \par\resizebox{17.5cm}{!}{\includegraphics[clip]{2889f04.eps}}\end{figure}$ Figure 4: Depth dependent fractional abundances for the models described in Table 1. The solid line corresponds to model 0, the dotted line is model 2, the dashed line is model 3. The dashed-dotted line is model 4 and the dashed-dotted-dotted line (model 6) corresponds to the best fitted X-ray model with an inner UV field of $G_{{\rm0,in}} = 10$ .
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In the text

$\begin{figure} \par\resizebox{17.45cm}{!}{\includegraphics[clip]{2889f05.eps}}\end{figure}$ Figure 5: Depth dependent fractional abundances for the models described in Table 1. The solid line corresponds to model 0, the dotted line is model 2, the dashed line is model 3. The dashed-dotted line is model 4 and the dashed-dotted-dotted line (model 6) corresponds to the best fitted X-ray model with an inner UV field of $G_{{\rm0,in}} = 10$ .
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In the text

$\begin{figure} \par\resizebox{17.2cm}{!}{\includegraphics[clip]{2889f06.eps}}\end{figure}$ Figure 6: Depth dependent fractional abundances for the models described in Table 1. The solid line corresponds to model 0, the dotted line is model 2, the dashed line is model 3. The dashed-dotted line is model 4 and the dashed-dotted-dotted line (model 6) corresponds to the best fitted X-ray model with an inner UV field of $G_{{\rm0,in}} = 10$ .
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In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f08.eps}}\end{figure}$ Figure 8: $\chi ^2$ values for the models 0-7 described in Table 1. The upper curve (solid line) corresponds to the $\chi ^2$ values calculated for all species, whereas the lower curve (dotted line) describes the values obtained considering only species that are influenced most by X-rays (see text). The $\chi ^2$ values are therefore smaller for the dotted curve.
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In the text

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{2889f09.eps}}\end{figure}$ Figure 9: $\chi ^2$ contour plots for the species influenced most by X-rays. The parameters in each plot that were not varied have been fixed at $L_{{\rm X}} = 10^{32}$ erg s^-1, $T_{{\rm X}} = 10^8$ K, $N_{{\rm H,in}} = 5 \times 10^{22}$ cm^-2 and $t \approx 5 \times 10^4$ yr (model 5). The contour levels are plotted for 0.7-2.4 in steps of 0.1.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{2889f10.eps}}\end{figure}$ Figure 10: $\chi ^2$ contour plot of $L_{{\rm X}}$ vs. $G_{{\rm0,out}}$ considering only species that are most sensitive to X-rays ( left) and contour plot $L_{{\rm X}}$ vs. $\zeta _{{\rm cr}}$ considering $\chi ^2$ values of HCO⁺ only ( right). The other parameters have been fixed at $T_{{\rm X}} = 10^8$ K and $N_{{\rm H,in}} = 5 \times 10^{22}$ cm^-2.
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In the text

$\begin{figure} \par\resizebox{17.5cm}{!}{\includegraphics[clip]{2889f11.eps}}\end{figure}$ Figure 11: Calculated H¹³CO⁺ line profiles for model 0 (solid line), model 1 (dotted line), model 3 (short dashed line), model 4 (dashed-dotted line) and model 5 (long dashed line). The H¹³CO⁺ 3-2 line (260 GHz) was convolved with a 18 $^{\prime \prime }$ JCMT beam, the H¹³CO⁺ 4-3 line (347 GHz) was convolved with a 14 $^{\prime \prime }$ JCMT beam and the H¹³CO⁺ 8-7 line (694 GHz) was convolved with a 8 $^{\prime \prime }$ JCMT beam.
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In the text

$\begin{figure} \par\resizebox{17.5cm}{!}{\includegraphics[clip]{2889f12.eps}}\end{figure}$ Figure 12: Calculated HCS⁺ line profiles for model 0 (solid line), model 1 (dotted line), model 3 (short dashed line), model 4 (dashed-dotted line) and model 5 (long dashed line). The HCS⁺ 6-5 line (256 GHz) was convolved with a 18 $^{\prime \prime }$ JCMT beam, the HCS⁺ 8-7 line (341 GHz) was convolved with a 14 $^{\prime \prime }$ JCMT beam and the HCS⁺ 10-9 line (427 GHz) was convolved with a 11 $^{\prime \prime }$ JCMT beam.
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In the text

$\begin{figure} \par\resizebox{17.5cm}{!}{\includegraphics[clip]{2889f13.eps}}\end{figure}$ Figure 13: Calculated H¹³CO⁺ line profiles for model 0 (solid line) and model 5 (dashed line) with a cosmic-ray ionization rate $\zeta _{{\rm cr}} = 5.6 \times 10^{-17}$ s^-1 and for model 0 (dotted line) and model 5 (dashed-dotted line) with a cosmic-ray ionization rate $\zeta _{{\rm cr}} = 3 \times 10^{-16}$ s^-1. The H¹³CO⁺ 3-2 line (260 GHz) was convolved with a 18 $^{\prime \prime }$ JCMT beam, the H¹³CO⁺ 4-3 line (347 GHz) was convolved with a 14 $^{\prime \prime }$ JCMT beam and the H¹³CO⁺ 8-7 line (694 GHz) was convolved with a 8 $^{\prime \prime }$ JCMT beam.
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In the text

$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{2889f07.eps}}\end{figure}$ Figure 7: Column density ratios for the inner $\approx$ 2000 AU ( $\approx$ 2 $^{\prime \prime }$ ) of the envelope. The models are described in Table 1.
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In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{2889f14.eps}}\end{figure}$ Figure C.1: Depth dependent fractional abundances for different X-ray temperatures $T{_{{\rm X}}}$ with $L_{{\rm X}} = 10^{32}$ erg s^-1 and $N_{{\rm H,in}} = 5 \times 10^{22}$ cm^-2 ( upper 6 figures) and for different inner column densities $N{_{{\rm H,in}}}$ with $L_{{\rm X}} = 10^{32}$ erg s^-1 and $T_{{\rm X}} = 7 \times 10^7$ K ( lower 6 figures).

In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{2889f15.eps}}\end{figure}$ Figure D.1: Depth dependent fractional abundances for different outer FUV fields $G_{{\rm0,out}}$ for model 0.

In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{2889f16.eps}}\end{figure}$ Figure D.2: Depth dependent fractional abundances for different cosmic-ray ionization rates for model 0 with $\zeta _{{\rm cr}} = 5.6 \times 10^{-17}$ s^-1 (solid line), for model 5 with $\zeta _{{\rm cr}} = 5.6 \times 10^{-17}$ s^-1 (dotted line), for model 5 with $\zeta _{{\rm cr}} = 10^{-17}$ s^-1 (dashed line) and for model 5 with $\zeta _{{\rm cr}} = 3 \times 10^{-16}$ s^-1 (dashed-dotted line).

In the text

$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f01.eps}}\end{figure}$	Figure 1: The photoionization cross sections for the elemental abundances given in Table A.1. The cross section for Compton scattering is calculated for hydrogen.
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f02.eps}}\end{figure}$	Figure 2: Physical and thermal structure of AFGL 2591. The power-law density distribution is adopted from the model of van der Tak et al. (1999). The gas temperature profile was calculated by Doty et al. (2002).
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f03.eps}}\end{figure}$	Figure 3: Ionization rates $\zeta _{{\rm H_2}}$ for the X-ray models presented in Table 1 and a constant cosmic-ray ionization rate $\zeta _{{\rm cr}} = 5.6 \times 10^{-17}$ s^-1. The arrow indicates the distance out to which an inner UV field is effective.
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$\begin{figure} \par\resizebox{17.5cm}{!}{\includegraphics[clip]{2889f04.eps}}\end{figure}$	Figure 4: Depth dependent fractional abundances for the models described in Table 1. The solid line corresponds to model 0, the dotted line is model 2, the dashed line is model 3. The dashed-dotted line is model 4 and the dashed-dotted-dotted line (model 6) corresponds to the best fitted X-ray model with an inner UV field of $G_{{\rm0,in}} = 10$ .
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$\begin{figure} \par\resizebox{17.45cm}{!}{\includegraphics[clip]{2889f05.eps}}\end{figure}$	Figure 5: Depth dependent fractional abundances for the models described in Table 1. The solid line corresponds to model 0, the dotted line is model 2, the dashed line is model 3. The dashed-dotted line is model 4 and the dashed-dotted-dotted line (model 6) corresponds to the best fitted X-ray model with an inner UV field of $G_{{\rm0,in}} = 10$ .
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$\begin{figure} \par\resizebox{17.2cm}{!}{\includegraphics[clip]{2889f06.eps}}\end{figure}$	Figure 6: Depth dependent fractional abundances for the models described in Table 1. The solid line corresponds to model 0, the dotted line is model 2, the dashed line is model 3. The dashed-dotted line is model 4 and the dashed-dotted-dotted line (model 6) corresponds to the best fitted X-ray model with an inner UV field of $G_{{\rm0,in}} = 10$ .
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$\begin{figure} \par\resizebox{8.8cm}{!}{\includegraphics[clip]{2889f08.eps}}\end{figure}$	Figure 8: $\chi ^2$ values for the models 0-7 described in Table 1. The upper curve (solid line) corresponds to the $\chi ^2$ values calculated for all species, whereas the lower curve (dotted line) describes the values obtained considering only species that are influenced most by X-rays (see text). The $\chi ^2$ values are therefore smaller for the dotted curve.
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$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{2889f09.eps}}\end{figure}$	Figure 9: $\chi ^2$ contour plots for the species influenced most by X-rays. The parameters in each plot that were not varied have been fixed at $L_{{\rm X}} = 10^{32}$ erg s^-1, $T_{{\rm X}} = 10^8$ K, $N_{{\rm H,in}} = 5 \times 10^{22}$ cm^-2 and $t \approx 5 \times 10^4$ yr (model 5). The contour levels are plotted for 0.7-2.4 in steps of 0.1.
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$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[clip]{2889f10.eps}}\end{figure}$	Figure 10: $\chi ^2$ contour plot of $L_{{\rm X}}$ vs. $G_{{\rm0,out}}$ considering only species that are most sensitive to X-rays ( left) and contour plot $L_{{\rm X}}$ vs. $\zeta _{{\rm cr}}$ considering $\chi ^2$ values of HCO⁺ only ( right). The other parameters have been fixed at $T_{{\rm X}} = 10^8$ K and $N_{{\rm H,in}} = 5 \times 10^{22}$ cm^-2.
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$\begin{figure} \par\resizebox{7.8cm}{!}{\includegraphics[clip]{2889f07.eps}}\end{figure}$	Figure 7: Column density ratios for the inner $\approx$ 2000 AU ( $\approx$ 2 $^{\prime \prime }$ ) of the envelope. The models are described in Table 1.
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