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Appendix A: Density diagnostic

In this section we study the influence of collisional rates on the modeling of the SiO and SiS lines observed in our line survey of Orion. Although most of the emission in Orion arises from regions of high volume density, the intensity of the high-velocity wings apparent in the SiO and SiS line profiles arise from a region, the plateau, in which the density is not enough to thermalize the rotational levels of high dipole moment molecules such as SiO (3.1 D) and SiS (1.73 D). Collisional rates are then needed for each species to derive the physical conditions. For SiO previous calculations by Green and collaborators (Bieniek & Green 1983; Turner et al. 1992; see http://www.giss.nasa.gov/data/mcrates#sio) have provided collisional rates for this molecule and temperatures 20−1500 K. These collisional rates have been recalculated using a new SiO-p-H₂ surface by Dayou & Balança (2006). However, no collisional rates were available of SiS until recently: Vincent et al. (2007) and Klos & Lique (2008) have calculated the state-to-state collisional rates for the system SiS-He and SiS-H₂, respectively.

We tested the influence of collisional rates on the modeling of the SiO and SiS lines observed in our line survey of Orion. Using the recent rates quoted above we computed line-intensity ratios between some transitions to provide tools for estimating the physical conditions in astrophysical sources. We covered volume densities between 10²−10⁹ cm^-3 and kinetic temperatures from 10 to 300 K including levels up to J = 20 for SiO and J = 40 for SiS. In the following, we analyze the excitation conditions for 1 → 0, 2 → 1, 3 → 2, 5 → 4, 12 → 11, and 19 → 18 for both molecules.

A.1. SiO

	Fig. A.1 Intensity ratio between two transitions for SiO as a function of H2 density with the SiO column densities equal to 1012, 1013, 1014, and 1015 cm-2 and temperatures from 10 K to 100 K.
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	Fig. A.2 Same as A.1 but for T = 300 K.
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	Fig. A.3 Comparison of the line intensities predicted using two different sets of collisional rates (see text) for different lines, column densities, and densities.
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The line-intensity ratios for SiO are shown in Figs. A.1 (kinetic temperature between 10 and 100 K) and A.2 (for a temperature of 300 K). In Fig. A.1 we notice that the intensity ratio T_B(3 → 2)/T_B(2 → 1) is particularly sensitive to densities of about 10⁴ to 10⁶ cm^-3, whereas for T_B(5 → 4)/T_B(1 → 0) it shows important variations in the density range 10⁶ to 10⁷ cm^-3. Using the intensity ratio T_B(5 → 4)/T_B(12 → 11), we can explore density values around 10⁷−5 × 10⁸ cm^-3. For T_K = 300 K and T_B(12 → 11)/T_B(19 → 18), we can trace densities above 10⁵ cm^-3, as seen in Fig. A.2. For lower densities, the 19−18 line will be very weak.

To illustrate this point, we deduce the intensity ratio T_B(2 → 1)/T_B(3 → 2) of SiO from our observations, and find  ≃ 2.6 (see Table 2), which corresponds, depending on the column density and for T_K = 100 K, on densities between 10^5.5 and 10⁷ cm^-3. Our results for the physical parameters of the different cloud components discussed in previous sections are given in Table 4.

The collisional rates calculated by Turner et al. (1992) have been used in the past to describe collisions of SiO molecules with H₂. We used the new rates of Dayou & Balança (2006) throughout this paper. As a first step in modeling SiO emission in warm clouds, we compared the results using both sets of collisional rates for a wide range of physical conditions: T_K = 10−300 K, N(SiO) = 10¹²−10¹⁵ cm^-2, and n(H₂) = 1−10⁹ cm^-3. Figure A.3 shows the brightness temperature (T_B) ratio (predictions using the Dayou & Balança 2006 rates over those obtained from Turner et al. 1992 rates) as a function of H₂ density for different values of the SiO column density and temperature and for the six first transitions of this molecule. The plots in Fig. A.3 show that the difference in the predicted line intensities between both sets of collisional rates never exceed 40% (J = 6−5 line), because it is always below 20% for all other rotational lines and kinetic temperatures. The lowest temperature for the collisional rates of Turner et al. (1992) is 20 K. We have extrapolated these rates to obtain the corresponding ones at 10 K. For most transitions the predicted line intensities from the Dayou & Balança (2006) rates are lower than those predicted from Turner et al. (1992) rates for densities below  ≃ 10⁵ cm^-3. Although the differences in line intensities are not significant for determining the physical properties of the emitting gas in interstellar clouds, we adopted in our SiO calculations the new rates of Dayou & Balança (2006).

A.2. SiS

	Fig. A.4 Intensity ratio between two transitions for SiS as a function of H2 density with the SiS column density equal to 1012, 1013, 1014, and 1015 cm-2.
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	Fig. A.5 Same as A.4 but for T = 300 K.
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	Fig. A.6 Same as A.3 for SiS with the SiS column density equal to 1012, 1013, 1014, and 1015 cm-2.
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We performed the same study for SiS using the rates calculated by Vincent et al. (2007). Figures A.4 and A.5 show our results. We observe the same trends as for SiO, but for lower densities. Thus, the T_B(3 → 2)/T_B(2 → 1) ratio increases in the density range 10³ to 10⁵ cm^-3, the second one T_B(5 → 4)/T_B(1 → 0) in 10⁴ to 10⁵ cm^-3, and the last graphs of Fig. A.4 show that T_B(5 → 4)/T_B(12 → 11) varies mostly between 10⁵ and a few 10⁶ cm^-3. In Fig. A.5, we can see that for T_K = 300 K, T_B(12 → 11)/T_B(19 → 18) are useful for densities around 10⁵ cm^-3. Two of those lines have been detected in our survey, the transitions 5 → 4 and 12 → 11, with an intensity ratio of  ≃ 0.12. For T_K = 100 K we can derive a volume density  ≃ 10^5.5 cm^-3.

Before 2007, no collisional data was available for SiS, so most authors have adopted the SiO collisional rates for SiS. As quoted above, the system SiS-He has been studied by Vincent et al. (2007). Lique et al. (2008) have compared these rates with the correspondings for the SiS-H₂ system. They show that, when scaled by the square root of the collision reduced mass, the SiS-He rates were a reasonable approximation to describe collisions with H₂. We have updated the LVG code by adding the new SiS-He and SiS-H₂ rates. We calculated the line intensities and compared the results to those obtained with rates for SiO from Turner et al. (1992) (multiplied by a factor 2 to take the larger geometrical size of the SiS molecule into account). Figure A.6 shows the line intensity ratio (brightness temperature obtained with rates from Vincent et al. 2007 over those calculated with rates from Turner et al. 1992) as a function of n(H₂) for the first six rotational transitions. The discrepancies in the line intensities between the two cases do not exceed 50%. As for SiO, we notice that the differencies between the two sets of collisional rates are the same for all column densities: the line intensity predicted with rates for SiS are lower than those predicted from Turner et al. (1992) rates for densities up to  ≃ 10³. These differences are quite small and do not affect the determination of the physical parameters performed by authors who previously used the Turner et al. (1992) rates in their models to interpret SiS observations. We also tried to describe SiS excitation by collisions with the rate coefficients for the system CS-He from Green & Chapman (1978) with an appropriate scaling factor. The predicted intensities show reasonable agreement with those derived from SiS-He or SiS-H₂ collisional rates. These results show that, with the actual calibration accuracy for the SiS observations, determination of the properties of the emitting gas is not very sensitive to small differences in collisional rates. It is a rather curious result that the predicted line intensities with both sets of collisional rates, deduced from two different potential energy surfaces, moreover, with different propensity rules, produce similar intensity ratios (when the scaling factor is adequately selected). Determining the SiS column densities, we used the SiS-H₂ rates (Klos & Lique 2008), although no significant differences were found when we used the SiS-He ones.

To better quantify the effects of the use of scaled SiO-He rates in predicting SiS intensities, we considered a case in which the lines are optically thin, for instance, n(H₂) = 10⁵ cm^-3, T_K = 40 K, and N(SiS) = 3 × 10¹² cm^-2. The predicted line intensities from SiS-He rates are T_B(2 → 1, 4 → 3, 6 → 5) = 0.08,

0.26, 0.33 K. To obtain these results from scaled SiO-He rates, we need a density of 7 × 10⁴ cm^-3, or must reduce the scaling factor from 2 to  ≃ 1.5, i.e., an error lower than two in density.

We compared predictions from the SiS-He rates with those obtained from the SiS-H₂ rates and found insignificant variation between both.

Appendix B: Online figures

Fig. B.1 Integrated intensity of the J = 5−4 transition of SiO at different velocity ranges (indicated at the top of each panel). In some panels, the integrated intensity of the maps has been multiplied by a scale factor (indicated in the panels) to maintain the same color dynamics for all maps. The step in integrated intensity () is 20 K km s-1 from 25 to 305 K km s-1 and the minimum contours are 5 and 15 K km s-1. See text (Sect. 2) for main beam antenna temperature correction.

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	Fig. B.2 Observed lines (histogram spectra) and model (thin curves) of  29SiS and SiS v = 1. The dashed line shows a radial velocity at 13.5 km s-1.
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	Fig. B.3 Observed lines of different molecules at a position (−15′′, 15′′) offset IRc2. The dashed line shows a radial velocity at 15.5 km s-1.
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	Fig. B.4 Observed lines (histogram spectra) and model (thin curves) of SiN.
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Appendix C: Online tables

© ESO, 2011