Herschel/HIFI detections of hydrides towards AFGL 2591 - Envelope emission versus tenuous cloud absorption

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Volume 521 (October 2010)

A&A, 521 (2010) L44

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Herschel/HIFI: first science highlights

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Issue		A&A Volume 521, October 2010 Herschel/HIFI: first science highlights


Article Number		L44
Number of page(s)		7
Section		Letters
DOI		https://doi.org/10.1051/0004-6361/201015098
Published online		01 October 2010

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Table 1: Observed lines in AFGL 2591.

Appendix A: Spectra of non-detections

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{15098fg2.eps} \end{figure}$	Figure A.1: Spectra observed towards AFGL 2591 without detection of target lines. The velocity is given relative to the systemic velocity $v_{\rm sys}$ = -5.5 km s^-1.
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Figure A.1 presents spectra without detected target lines, given in Table 1. For clarity, the spectra of CH( 5/2_3,+-3/2_2,-) and OH⁺( 2_1,3/2-1_1,3/2) have been scaled by a factor of 0.1. In the spectrum of CH( 5/2_3,+-3/2_2,-), the H₂O( 2₂₁-2₁₂) line is detected, which will be presented in an upcoming paper (van der Tak et al., in preparation). The H₂O⁺( 2_02,3/2-1_11,3/2) spectrum contains a SO₂ line with upper level energy similar to the lines detected by van der Tak et al. (2003) in the same source. In the other sideband of the NH⁺( 3/2₊-1/2_-) spectrum, the OH⁺( 2_1,3/2-1_1,3/2) line is seen. In the upper side band of the SH⁺( 1_2,5/2-0_1,3/2) line, the HCO⁺(6-5) line has been detected. The velocity range of ${\pm}40$ km s^-1 corresponds to a frequency range of ${\pm}67$ MHz at 500 GHz and ${\pm}253$ MHz at 1900 GHz. Thus, the lines should be seen in the spectra, even if the predicted rest frequency is grossly wrong.

Appendix B: Modeling the line spectra

This Appendix gives the equations used to model the line spectra. The intensity $T^{\rm model}(\nu)$ [K] at frequency $\nu$ for a slab of N emitting or absorbing layers in front of a continuum source is obtained from

$\displaystyle % T^{\rm model}(\nu)$	=	$\displaystyle T^{\rm continuum}(\nu) {\rm e}^{-\sum_{i=1}^N \Delta \tau^i(\nu)}$
		$\displaystyle + ~ \sum_{i=1}^N \frac{c^2}{2 \nu_0^2 k} B_{\nu_0}(T^i_{\rm ex}) ... ..._{j=1}^{i-1} \Delta \tau^j(\nu)} \left(1-{\rm e}^{-\Delta \tau^i(\nu)} \right),$	(B.1)

Table B.1: Hyperfine components used to model the spectra.

with the (background) continuum intensity $T^{\rm cont}(\nu)$ , the opacity per layer $\Delta \tau^i(\nu)$ , the frequency of the component $\nu_0$ with the largest Einstein-A coefficient and the Planck function $B_\nu(T)$ . Note that this equation assumes a covering factor of 100% for each layer and the same excitation temperature for all hyperfine/fine components. The line opacity is calculated from the sum over the M fine/hyperfine components of the transition,

$\begin{displaymath}% \tau^i(\nu)=N_{\rm mol}^i \ \sum_{k=1}^M \ \frac{c^2}{8 \pi... ...rm u}}{g_{\rm l}} - x^{i,k}_{\rm u} \right) \ \phi^{i,k}(\nu), \end{displaymath}$

(B.2)

with the column density per layer $N_{\rm mol}^i$ , the Einstein-A coefficient $A_{\rm ul}^k$ , the normalized line profile function $\phi^{i,k}(\nu)$ , the normalized level population of the upper and lower level ( $x^{i,k}_{\rm u}$ and $x^{i,k}_{\rm l}$ , respectively) and the statistical weights ( $g_{\rm u}$ and $g_{\rm l}$ , respectively). The normalized level population per layer is a Boltzmann distribution for the temperature $T^i_{\rm ex}$ . The line profile function $\phi^{i,k}(\nu)$ is assumed to be a Gaussian with width $\Delta v^i$ (FWHM) centered at the frequency of the component minus the velocity $v_{\rm lsr}^i$ of the layer.

The free parameters per layer are thus the excitation temperature $T^i_{\rm ex}$ , the column density $N_{\rm mol}^i$ , the width $\Delta v^i$ and the velocity $v_{\rm lsr}^i$ . Two layers are used for CH, H₂O⁺, OH⁺ and NH with a red-shifted layer in front of a blue-shifted layer. Three layers are used for CH⁺ with a layer centered at the source velocity between the background continuum and the blue-shifted layer. To constrain the parameters of the layer, the least squares of the modeled to the observed spectra are minimized.

Molecular data of the individual hyperfine components of CH, OH⁺, NH and H₂O⁺ used to model the line spectra in Fig. 1 are given in Table B.1. The table gives the frequency, Einstein-A coefficient ( $A_{\rm ul}$ ), the upper level energy ( $E_{\rm u}$ ) and the statistical weights of the upper and lower level of the transition ( $g_{\rm u}$ and $g_{\rm l}$ , respectively). The third column refers to the velocity shift in km s^-1 of the component relative to the one with the largest Einstein-A coefficient. The component with the largest Einstein-A coefficient is marked by (*).

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