Volume 521, October 2010
Herschel/HIFI: first science highlights
Article Number L40
Number of page(s) 7
Section Letters
Published online 01 October 2010

Online Material

The authors are grateful to many funding agencies and the HIFI-ICC staff who has been contributing for the construction of Herschel and HIFI for many years. HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada and the United States under the leadership of SRON Netherlands Institute for Space Research, Groningen, The Netherlands and with major contributions from Germany, France and the US. Consortium members are: Canada: CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS; Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri- INAF; Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astronómico Nacional (IGN), Centro de Astrobiología (CSIC-INTA). Sweden: Chalmers University of Technology - MC2, RSS & GARD; Onsala Space Observatory; Swedish National Space Board, Stockholm University - Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA: Caltech, JPL, NHSC.

Appendix A: Radex model

Figure A.1 shows the CO 6-5/10-9 line ratios for a slab model with a range of temperatures and densities.

\end{figure} Figure A.1:

Model line ratios of CO 6-5/10-9 for a slab model with a range of temperatures and densities. The adopted CO column density is 1017 cm-2 with a line width of 10 km s-1, comparable to the inferred values. For these parameters the lines involved are optically thin. The colored lines give the range of densities within the 20'' beam for the three sources based on the models of Jørgensen et al. (2002).

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Appendix B: Abundance profiles for IRAS 2A

Among the three sources, IRAS 2A has been selected for detailed CO abundance profile modeling because more data are available on this source, and because its physical and chemical structure has been well characterized through the high angular resolution submillimeter single dish and interferometric observations of Jørgensen et al. (2005a,2002). The physical parameters are taken from the continuum modeling results of Jørgensen et al. (2002). In that paper, the 1D dust radiative transfer code DUSTY (Ivezic & Elitzur 1997) was used assuming a power law to describe the density gradient. The dust temperature as function of radius was calculated self-consistently through radiative transfer given a central source luminosity. Best-fit model parameters were obtained by comparison with the spectral energy distribution and the submillimeter continuum spatial extent. The resulting envelope structure parameters are used as input to the Ratran radiative transfer modeling code (Hogerheijde & van der Tak 2000) to model the CO line intensities for a given CO abundance structure through the envelope. The model extends to 11000 AU from the protostar, where the density has dropped to $2\times 10^4$ cm-3. The CO-H2 collisional rate coefficients of Yang et al. (2010) have been adopted.

The C18O lines are used to determine the CO abundance structure because the lines of this isotopologue are largely optically thin and because they have well-defined Gaussian line shapes originating from the quiescent envelope without strong contaminations from outflows. Three types of abundance profiles are examined, namely ``constant'', ``anti-jump'' and ``drop'' abundance profiles. Illustrative models are shown in Fig. B.1 and the results from these models are summarized in Table B.1.

\par\includegraphics[scale=0.35, angle=270]{15119fgB1.eps}\vspace{-2mm}
\end{figure} Figure B.1:

Examples of constant, anti-jump, and drop abundance profiles for IRAS 2A for $T_{\rm ev} =25$ K and $n_{\rm de} =7 \times 10^4$ cm-3.

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Table B.1:   Summary of CO abundance profiles for IRAS 2A.

B.1 Constant abundance model

The simplest approach is to adopt a constant abundance across the entire envelope. However, with this approach, and within the framework of the adopted source model, it is not possible to simultaneously reproduce all line intensities. This was already shown by Jørgensen et al. (2005c). For lower abundances it is possible to reproduce the lower-J lines, while higher abundances are required for higher-J lines. In Fig. B.2 the C18O spectra of a constant-abundance profile are shown for an abundance of $X_0 =1.4 \times 10^{-7}$, together with the observed spectra of IRAS 2A. Based on these results, the constant-abundance profile is ruled out for all three sources.

B.2 Anti-jump abundance models

The anti-jump model is commonly adopted in models of pre-stellar cores without a central heating source (e.g., Tafalla et al. 2004; Bergin & Snell 2002). Following Jørgensen et al. (2005c), an anti-jump abundance profile was employed by varying the desorption density, $n_{\rm de}$, and inner abundance $X_{\rm in} = X_{\rm D}$ in order to find a fit to our observed lines. Here, the outer abundance X0 was kept high at $5.0 \times 10^{-7}$ corresponding to a 12CO abundance of $2.4 \times 10^{-4}$ for 16O/18O = 550 as was found appropriate for the case of IRAS 2A by Jørgensen et al. (2005c). This value is consistent with the CO/H2 abundance ratio determined by Lacy et al. (1994) for dense gas without CO freeze-out.

The best fit to the three lowest C18O lines (1-0, 2-1 and 3-2) is consistent with that found by Jørgensen et al. (2005c), corresponding to $n_{\rm de} =7 \times 10^4$ cm-3 and $X_{\rm D}=3\times 10^{-8}$ (CO abundance of $1.7\times
10^{-5}$). In the $\chi ^2$ fits, the calibration uncertainty of each line (ranging from 20 to 30%) is taken into account. These modeled spectra are overplotted on the observed spectra in Fig. B.2 as the blue lines, and show that the anti-jump profile fits well the lower-J lines but very much underproduces the higher-J lines.

The value of X0 was verified a posteriori by keeping $n_{\rm de}$ at two different values of $3.4 \times 10^{4}$ and $7 \times 10^{4}$ cm-3. This is illustrated in Fig. B.3 where the $\chi ^2$ contours show that for both values of $n_{\rm de}$, the best-fit value of X0 is $\sim$ $5 \times 10^{-7}$, the value also found in Jørgensen et al. (2005c). The $\chi ^2$ contours have been calculated from the lower-J lines only, as these are paramount in constraining the value of X0. Different $\chi ^2$ plots were made, where it was clear that higher-J lines only constrain $X_{\rm D}$, as expected. The effect of $n_{\rm de}$ is illustrated in Fig. B.4 for the two values given above.

\end{figure} Figure B.2:

Best fit constant (green), anti-jump (blue) and drop abundance (red) Ratran models overplotted on the observed spectra. All spectra refer to single pointing observations. The calibration uncertainty for each spectrum is around 20-30$\%$and is taken into account in the $\chi ^2$ fit. See Table B.1 for parameters.

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\par\mbox{\includegraphics[scale=0.24]{15119fgB3a.eps} \includegraphics[scale=0.24]{15119fgB3b.eps} }\end{figure} Figure B.3:

The $\chi ^2$ plots for the anti-jump profiles where X0 and $X_{\rm D}$ values are varied. Right: for $n_{\rm de} =7 \times 10^4$ and left: for $n_{\rm de} = 3.4 \times 10^{4}$ cm-3. The asterisk indicates the value for Jørgensen et al. (2005c) used here. Contours are plotted at the 2$\sigma $, 3$\sigma $, and 4$\sigma $ confidence levels (left) and 3$\sigma $ and 4$\sigma $ confidence levels (right).

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\par\mbox{\includegraphics[scale=0.245]{15119fgB4a.eps} \includegraphics[scale=0.245]{15119fgB4b.eps} }\end{figure} Figure B.4:

The IRAS 2A spectra for the X0 and $X_{\rm D}$ parameters corresponding to the values in Jørgensen et al. (2005c) for different $n_{\rm de}$ values of $3.4 \times 10^{4}$ and $7 \times 10^{4}$ cm-3 .

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\par\mbox{\includegraphics[scale=0.24]{15119fgB5a.eps} \includegraphics[scale=0.24]{15119fgB5b.eps} }\end{figure} Figure B.5:

Reduced $\chi ^2$ plots and best-fit parameters (indicated with *) for the anti-jump model fit to the lines of C18O 1-0, 2-1, 3-2, 6-5 and 9-8 (right) and for the drop abundance model fit to the higher-J lines of C18O 6-5 and 9-8 (left). Contours are plotted at the 1$\sigma $, 2$\sigma $, 3$\sigma $, and 4$\sigma $ confidence levels.

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B.3 Drop-abundance profile

In order to fit the higher-J lines, it is necessary to employ a drop-abundance structure in which the inner abundance $X_{\rm in}$ increases above the ice evaporation temperature $T_{\rm ev}$ (Jørgensen et al. 2005c). The abundances $X_{\rm D}$ and X0 for $T<T_{\rm ev}$ are kept the same as in the anti-jump model, but $X_{\rm in}$ is not necessarily the same as X0. In order to find the best-fit parameters for the higher-J lines, the inner abundance $X_{\rm in}$ and the evaporation temperature $T_{\rm ev}$ were varied. The $\chi ^2$ plots (Fig. B.5, left panel) show best-fit values for an inner abundance of $X_{\rm
in}= 1.5 \times 10^{-7}$ and an evaporation temperature of 25 K (consistent with the laboratory values), although the latter value is not strongly constrained. These parameters fit well the higher-J C18O 6-5 and 9-8 lines (Fig. B.2). The C18O 5-4 line is underproduced in all models, likely because the larger HIFI beam picks up extended emission from additional dense material to the northeast of the source seen in BIMA C18O 1-0 map (Volgenau et al. 2006).

Because the results do not depend strongly on $T_{\rm ev}$, an alternative approach is to keep the evaporation temperature fixed at 25 K and vary both $X_{\rm in}$ and $X_{\rm D}$ by fitting both low- and high-J lines simultaneously. In this case, only an upper limit on $X_{\rm D}$ of $\sim$ $4 \times 10^{-8}$ is found (Fig. B.5, right panel), whereas the inferred value of $X_{\rm in}$ is the same. This figure conclusively illustrates that $X_{\rm in}>X_{\rm D}$, i.e., that a jump in the abundance due to evaporation is needed.

The above conclusion is robust within the context of the adopted physical model. Alternatively, one could investigate different physical models such as those used by Chiang et al. (2008), which have a density enhancement in the inner envelope due to a magnetic shock wall. This density increase could partly mitigate the need for the abundance enhancement although it is unlikely that the density jump is large enough to fully compensate. Such models are outside the scope of this paper. An observational test of our model would be to image the N2H+ 1-0 line at high angular resolution: its emission should drop in the inner $\sim$900 AU ($\sim$4 $\hbox{$^{\prime\prime}$ }$) where N2H+ would be destroyed by the enhanced gas-phase CO.

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