EDP Sciences
Free Access
Volume 562, February 2014
Article Number A83
Number of page(s) 20
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/201322386
Published online 12 February 2014

Online material

Appendix A: Radiative transfer modelling

Our one-dimensional spherical source model consists in two-layers with uniform density and kinetic temperature. The inner layer, close to the protostar, has a radius of 104 AU, a dust temperature of 30 K, and a total (front + back) column density N(H2) = 6.6 × 1022  cm-2 – hence, a density – and we assume this layer does not contain gas-phase nitrogen hydrides. Furthermore, the dust opacity is assumed to vary as a power-law of the wavelength, with a spectral index (β) of 2.8 and a dust opacity at 250 GHz of 1 g  cm-2. The values of N(H2) and β were adjusted so that the continuum observed with HIFI towards that source is reproduced well by our model.

The external layer has the same H2column density, so that the total column density is 1.3   ×   1023  cm-2 or 140 mag of visual extinction. We modelled the emergent telescope-convolved spectrum of all the observed transitions of ammonia, by solving the radiative transfer with the Monte-Carlo code RATRAN (Hogerheijde & van der Tak 2000). The collisional rates for NH3-H2(p) are taken from Maret et al. (2009). The o/p of NH3 was fixed at 0.7, as predicted by our chemistry model. The free parameters are the density, the gas temperature, and the NH3 column density in the external, absorbing, layer. The radii are set by the H2column density and the density of that layer. The emergent spectra were then fitted simultaneously to match the observed ones, and a χ2 used to select the best-fit model. We found that the self-absorbed profile of the 1−0 transition tightly constrains the H2density in the outer layer to less than 104  cm-3, since for higher densities the predicted profile no longer shows absorption. As a result, the absorbing ammonia molecules reside in the most external layer of the circumbinary envelope of IRAS 16293-2422.

thumbnail Fig. A.1

Comparison between the observed NH3 spectrum (black) from Hily-Blant et al. (2010a) and the best-fit model (red). The + and signs in the transition labelling are the same as in Maret et al. (2009).

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thumbnail Fig. A.2

Same as in Fig. A.1 for the NH multiplets, using the same physical model as for NH3 and adopting a single NH column density of 2.2 ± 0.8 × 1014  cm-2.

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An ensemble of solutions is then found for the ammonia column density and the kinetic temperature, with the best agreement corresponding to N(NH3) = 1.4   ×   1015  cm-2 and T =11 K, respectively (see Fig. A.1). This column density is a factor of 2.5 below the lower limit of Hily-Blant et al. (2010a). A cross-check of the best agreement was performed by computing the emergent hyperfine spectra of NH. To this aim, we used the LIME radiative transfer code (Brinch & Hogerheijde 2010), which takes line blending into account. The collisional rates for NH-H2(p) are scaled from the NH-He rates of Dumouchel et al. (2012) by applying the standard reduced mass ratio of 1.33. The model that best reproduces the three hyperfine multiplets of NH (see Fig. A.2) has a column density of NH in the foreground layer of 2.0   ×   1014  cm-2, in excellent agreement with the determination of Bacmann et al. (2010) based on the “HFS” method of the CLASS software. Therefore this simple 2-layers model succesfully reproduces both the NH and NH3 spectra. The NH2(o) column density was not re-analysed owing to the lack of collisional rates. However, the column density of NH2(o) was derived by Hily-Blant et al. (2010a) using the same method and under the same assumptions as those for NH by Bacmann et al. (2010), and is thus expected to be reliable as well. In addition, here, we assumed an o/p(NH2) of 2 to estimate the total column density of NH2.

Appendix B: Chemical updates

Table B.1

New ion-neutral chemical reaction rates and ortho-para branching ratios.

Table B.2

New dissociative recombination (DR) reaction rates and branching ratios.

Table B.3

Neutral-neutral chemical reaction rates and branching ratios considered.

© ESO, 2014

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