Free Access
Volume 494, Number 2, February I 2009
Page(s) 637 - 646
Section Interstellar and circumstellar matter
Published online 20 November 2008

Online Material

  Appendix A: RADEX - construction of a dust model

In order to relate the molecular column densities, N(x) of species x, to fractional abundances, X(x) = $N({x})/N({\rm H}_2)$, a uniform, homogeneous sphere of diameter L =  $N({\rm H}_2)/n({\rm H}_2)$ is assumed here. The adopted physical diameter of the PDR corresponding to an angular diameter of 120 $^{\prime \prime }$ (Sect. 3) at a distance of 910 pc is 0.53 pc. This is assumed to be equal to the line-of-sight depth.

The observed intensity of the continuum is used to estimate the internal radiation field sensed by the molecules. We construct a simple model of the broad-band spectrum at submm and far-infrared wavelengths in order both to characterise the internal radiation and to estimate the total column densities of dust and hydrogen. Thronson et al. (1983) measured the far-infrared emission of S140 and found a peak flux density of the order of 104 Jy slightly shortward of $\lambda$100 $\mu$m in a 49 $^{\prime \prime }$ beam. Minchin et al. (1995) presented total broad-band fluxes in a $1\hbox{$.\mkern-4mu^\prime$ }5$ $\times $ $1\hbox{$.\mkern-4mu^\prime$ }5$ box. We represent the latter results with a two-component model of thermal emission by dust over a solid angle of $\Omega = 1.9$ $\times $ 10-7 sr. The main component has a dust temperature $T_{\rm dust}$ = 40 K and a long-wavelength ( $\lambda > 40~\mu$m) form of the opacity law

\begin{eqnarray*}\tau_{\rm dust} = 0.0679 (100/\lambda)^{1.2}

where $\lambda$ is the wavelength in $\mu$m. The opacity law is smoothly matched to a standard interstellar extinction law at shorter wavelengths, which is also used to describe the second component at $T_{\rm dust}$ = 140 K. The opacity of the first dust component corresponds to a visual extinction $A_{\rm V}$ = 58.8 mag. The second component has a smaller optical depth $A_{\rm V}$ = 0.023 mag, but is assumed to cover the same solid angle. In addition, the mid-infrared measurements of Ney & Merrill (1980) have been adapted in order to specify the radiation field at even shorter wavelengths. In the calculations, the molecules are assumed to be exposed to an average intensity of continuous radiation

\begin{eqnarray*}I_{\nu} = B_{\nu}(T_{\rm CMB}) + \eta {{f_{\nu}^{~ \rm dust}}\over

where $B_{\nu}$ is the Planck function, $T_{\rm CMB}$ = 2.73 K is the temperature of the cosmic background radiation, $f_{\nu}^{~ \rm dust}$ is the flux density of the 2-component dust model, $\Omega$ = 1.9 $\times $ 10-7 sr, and $\eta$ = 0.72 is a dilution factor to scale the brightness of the dust source to the larger beam area of the Odin measurements. It is important to keep in mind that we observe this strong far-infrared radiation; therefore, the co-extensive molecules must sense it also.

For the adopted interstellar extinction law and a standard gas/extinction ratio,

\begin{eqnarray*}2 N({\rm H}_2) = 1.6\times 10^{21} A_{\rm V} ~~{\rm cm}^{-2},

the adopted dust model implies $N({\rm H_2})$ = 4.7 $\times $ 1022 cm-2 and an average density $n({\rm H}_2)$ = 2.9 $\times $ 104 cm-3 over the source size L = 0.53 pc. This average density is, however, inconsistent with the observed molecular line emission in large beams ( $\theta \geq 1'$). Although a uniform RADEX model can be constructed based upon this density, the line-centre optical depths of the pure rotational lines of H2O and NH3 would be of the order of 200 and 100, respectively. Such large opacities would imply significant line broadening through saturation of the emission, which conflicts with the observed narrow profiles of $\sim$3 km s-1.

Appendix B: Figures and tables

\end{figure} Figure B.1:

Odin observations of H218O in the central position.

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\end{figure} Figure B.2:

Rotation diagram of the broad component of 13CO(1-0) with the Onsala 20-m telescope, J = 2-1 and J = 3-2 from Minchin et al. (1993), and J = 5-4 with Odin, producing $T_{\rm ROT}$ = 24 $\pm $ 2 K and $N_{\rm ROT}$ = (2.5 $\pm $ 0.4) $\times $ 1016  cm-2.

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\end{figure} Figure B.3:

Rotation diagram of the narrow component of 13CO(2-1) and J = 3-2 from Minchin et al. (1993), J = 5-4 with Odin, and J = 6-5 from Graf et al. (1993), producing $T_{\rm ROT}$ = 69 $\pm $ 27 K and $N_{\rm ROT}$ = (3.2 $\pm $ 1.8) $\times $ 1016  cm-2. J = 1-0 is not included in the fit.

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\end{figure} Figure B.4:

Gaussian fits to 13CO(5-4) at the central position. The widths, amplitudes and centre velocities are 3.2  km s-1 and 8.2  km s-1; 6.610 K and 0.612 K; -7.3  km s-1 and -6.8  km s-1, respectively.

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\end{figure} Figure B.5:

Gaussian fits to the convolved (to the Odin 126 $^{\prime \prime }$ beam) spectra of 13CO(1-0) at position 1. The widths, amplitudes and centre velocities are 2.7  km s-1 and 8.6  km s-1; 6.982 K and 0.395 K; -7.6  km s-1 and -8.0  km s-1, respectively.

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\end{figure} Figure B.6:

Gaussian fits to H2O at the central position. The widths, amplitudes and centre velocities are 3.1  km s-1 and 8.8  km s-1; 416 mK and 213 mK; -7.1  km s-1 and -6.1  km s-1, respectively.

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\end{figure} Figure B.7:

Gaussian fits to NH3 at the central position. The widths, amplitudes and centre velocities are 3.3  km s-1 and 8.5  km s-1; 487 mK and 100 mK; -7.6  km s-1 and -6.4  km s-1, respectively.

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Table B.1:   Observed transitions and their parametersa in S140 with the Odin satellite in a five point NE-SW strip.

Table B.2:   13CO Gaussian fitsa. $T_{\rm b}$ uses a source size for the PDR (narrow component) of 120 $^{\prime \prime }$  $\rightarrow \eta _{\rm bf}$ = 2, and a source size for the broad outflow component of 85 $^{\prime \prime }$  $\rightarrow \eta _{\rm bf}$ = 3.

Table B.3:   H2O Gaussian fitsa. $T_{\rm b}$(PDR) uses a source size of 120 $^{\prime \prime }$  $\rightarrow \eta _{\rm bf}$ = 2, while $T_{\rm b}$(outflow) uses a source size of 85 $^{\prime \prime }$  $\rightarrow \eta _{\rm bf}$ = 3.

Table B.4:   NH3 Gaussian fitsa. $T_{\rm b}$(PDR) uses a source size of 120 $^{\prime \prime }$  $\rightarrow \eta _{\rm bf}$ = 2, while $T_{\rm b}$(outflow) uses a source size of 85 $^{\prime \prime }$  $\rightarrow \eta _{\rm bf}$ = 3.

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