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Up: A survey of SiO


Subsections

4 Results

Our main results are given in tables and spectral figures, which are available in electronic form in the address given on the title page of this article. The tables contain the selected sources and the observed SiO line parameters. The associated H2O maser line properties, when available in the Arcetri or B&E catalogues, are also included. The SEST and Onsala observations are listed separately, which results in two tables (B.1 and B.2), the first pages of which are shown in Appendix B. The entries are arranged according to increasing right ascension.

The columns of Tables B.1 and B.2 are: (1) source number, name, galactic coordinates (l,b) and distance, for detected sources the name is printed in boldface characters; (2) 1950.0 equatorial coordinates; (3) observed transition plus the reference of the maser catalogue (usually Arcetri (Arc.) or Braz & Epchtein 1983 (B&E)); (4) peak antenna temperatures $T_{\rm A}^*$ of the SiO lines (if detected) and the measured maximum flux density of the H2O maser (or sometimes OH maser, in which case clearly indicated); (5) rms noise of the original SiO and the H2O spectra; (6) peak velocities $V_{\rm peak}$ of the SiO lines and the velocity of the strongest maser component; (7) detected minimum velocities $V_{\rm min}$ of the SiO emission and maser features (when reliably determined and listed); (8) the corresponding maximum velocities $V_{\rm max}$; (9) velocity centroids $V_{\rm cen}$ of the SiO emission and maser features ($\equiv (V_{\rm min} +
V_{\rm max})/2$); (10) intensity weighted average velocity $V_{\rm mean}$for SiO; (11) full width (FW) of the detected SiO lines and maser emission features ($\equiv V_{\rm max} - V_{\rm min}$); (12) SiO line widths (variance or the second moment); (13) the integrated intensities of the SiO lines and the integrated flux density of the maser line (if available); (14) asymmetry parameter P of the SiO lines defined as $2 \,(V_{\rm peak} - V_{\rm
cen})/FW$, and the velocity of the associated molecular cloud ($V_{\rm
cloud}$) found in the literature; (15) References to other surveys and association with a known object within $20^{\prime\prime}$. The key for the reference codes are given on the first pages of Tables B.1 and B.2. A reference is given without brackets if the positional coincidence is better than $5^{\prime\prime}$, and in brackets if the difference between the used coordinates is $5-20^{\prime\prime}$.

When no reference is given the distance in Col. (1) is a kinematic distance calculated from the cloud velocity given in Col. (14) by using the galactic rotation curve determined by Brand & Blitz (1993) for R0 =8.5 kpc and $\Theta_0 = 220$ km s-1. For sources in the first and fourth quadrants with a distance ambiquity the near kinematic distance was assumed. The reference codes of photometric distances are explained in the bottom of the first page of each table. A hyphen (-) means that no solution has been found with the kinematical model, nor any reference to a photometric distance. The cloud velocity, $V_{\rm
cloud}$, refers usually to the velocity of the associated dense core as estimated from CS data. When the latter has not been available, a radial velocity determined from NH3 or CO observations has been used. The references are given below the distance references in Tables B.1 and B2. If no molecular line measurements has been found in the literature we have used for the kinematic distance estimate the peak radial velocity of the SiO(J=2-1) line from the present survey or the peak velocity of the associated maser. In this case the corresponding field in Col. (14) is empty.

All the detected SiO lines are presented in the spectral figures since the line shape changes considerably from source to source and contains information on the nature of the associated shock. The spectra can be identified with the entries of Tables B.1 and B.2 by the source number and name. The first nine detections (in order in the tables) of the SEST and Onsala surveys are shown in Appendix B.

The H2O maser velocity ranges and the peak velocities from the Arcetri catalogue are indicated in the spectral figures. For H2O masers with $\delta < -30^\circ$ only the peak velocities are marked, which are available in B&E. For several southern sources the velocity range of the 18-cm OH maser features found in the literature is also indicated.

4.1 Detection rate

Table 2 indicates the detection rates with the SEST and the Onsala telescope for three different source categories: 1.3-cm H2O masers, OH masers and IRAS sources with colours typical of ultracompact HII-regions.


  
Table 2: Numbers of observed H2O masers, OH masers and UC HII regions and SiO detections with SEST and Onsala

\begin{tabular}
{lcccc}
\hline
 & H$_2$O & OH & UC HII \\  \hline
 SEST & & & \\...
 ...e detections & {\bf 109}$^*$\space & {\bf 5} & {\bf 18} \\  
\hline\end{tabular}
*Three H2O maser sources were observed with both telescopes and two of them were detected.


In addition, SiO was detected with Onsala towards 3 of the 11 dust continuum emission peaks near H2O masers from the survey of Jenness et al. (1996), and towards the CS(7-6) position in S76E from the survey of Plume et al. (1992). The total number of detections is 136. With the SEST the detection was always made in both J=2-1 and J=3-2 transitions, except towards the source No. 164 (OH19.48+0.16), where only J=2-1 was detected. The intensity ratios of these two lines are discussed in a later section.

According to Table 2 there is a clear difference in the overall detection rates between the Onsala telescope and the SEST. Only 22 percent of the target sources were detected in SiO with Onsala, whereas the detection rate with SEST is 52 percent. The effective apertures and the achieved RMS noise levels are similar for both telescopes. It is conceivable, therefore, that the difference in detection rates is due to the properties of the selected target sources. In the following we shall discuss their galactic distribution, the flux densities of the associated H2O masers, and the far-infrared flux densities and luminosities of the associated IRAS point sources.

The median values of the derived and adopted distances are 3.0 kpc and 3.3 kpc for the SEST and Onsala samples, respectively. The lower detection rate with Onsala is therefore not caused by the fact that the target sources would be on the average further away.

In Fig. 1, the detection rate as a function of the galactic longitude is graphed as a histogram showing the number of observations and detections for $30^\circ$ wide intervals. The longitude ranges covered by the SEST and Onsala observations are indicated. The SEST target sources are mostly concentrated to the galactic plane, whereas the sources observed with Onsala have larger scatter in the galactic latitude. This can be seen by comparing the histograms in Fig. 1a, which represents all observed and detected sources, and in Fig. 1b, where only sources within $2^\circ$ from the galactic plane are included. It is evident from both figures, that the detection rate is the highest in the galactic longitude range $300^\circ
\leq l < 30^\circ$. Outside this range there is no great difference between the detection rates with Onsala and the SEST.

  
\begin{figure}
\vspace*{-5mm}
\centering
\psfig {file=fig1.eps,width=8.8cm,bbllx=50pt,bblly=50pt,bburx=550pt,bbury=850pt,angle=0}\end{figure} Figure 1: Number of observed sources and SiO detections as a function of the galactic longitude a) for all sources and b) for sources within $2^\circ$ from the galactic plane. The longitude ranges covered by the SEST and Onsala observations are indicated

The projected distribution of the observed and detected sources in the galactic plane is shown in Fig. 2. The SEST and Onsala target sources are denoted by different markers. The solar circle and a circle with a radius of 3 kpc are indicated in the figure. The latter circle roughly corresponds to the inner boundary of the so called "molecular ring'' between galactocentric distances 3 and 7 kpc with a large H2 surface density as determined from CO observations (Dame et al. 1987; Blitz 1997). Almost all sources (96%) in the sector defined by $330^\circ \leq l \leq 30^\circ$ belong to the "molecular ring'' and the percentage is high (73%) also in the neighbouring $30^\circ$ wide sectors i.e. $300^\circ \leq l < 330^\circ$ and $30^\circ < l \leq 60^\circ$. The average galactocentric distances in these regions are 5.5 kpc ($\vert l\vert \leq 30^\circ$) and 6.5 kpc ($30^\circ < \vert l\vert \leq
60^\circ$).

  
\begin{figure}
\vspace*{-3cm}
\centering
\psfig {file=fig2.eps,width=8.5cm,bbllx=50pt,bblly=80pt,bburx=550pt,bbury=800pt,angle=0}\end{figure} Figure 2: A "face-on'' view of the distribution of the observed and detected sources. The SEST survey objects are denoted by squares and the Onsala survey objects are denoted by triangles. Filled markers indicate detections. The locations of the sun and the galactic centre are denoted by $\odot$ and a cross, respectively. The SEST survey covers the half-plane from $l = 210^\circ$ to $l = 30^\circ$. The direction $l = 330^\circ$ is denoted by a dashed line. The solar circle and the galactocentric radius 3 kpc are also indicated

The distribution of the detection rate as a function of the galactocentric radius is plotted in Fig. 3. All H2O and OH masers and IRAS sources with colours typical of UC HII regions are included. It can be seen in this figure that the detection rate is higher among sources within the solar circle than for those located in the outer Galaxy.

  
\begin{figure}
\centering
\psfig {file=fig3.eps,width=8.8cm,bbllx=50pt,bblly=50pt,bburx=520pt,bbury=800pt,angle=270}

\vspace{4mm}\end{figure} Figure 3: Number of observed and detected sources as a function of the galactocentric radius. All masers and IRAS sources fulfilling the colour criteria of UC HII regions are included

Examination of the individual source properties reveals that the detection rate is the highest towards intense H2O masers. This tendency is illustrated in Fig. 4, which shows a histogram of the detection rate as a function of H2O maser peak flux density. For Arcetri sources the maximum H2O flux density has been taken in case several measurements are listed. One can see in the diagram that the detection percentage is about 60 or higher when the maser peak flux density exceeds 100 Jy. The Onsala sample contains 40 masers with peak flux densities less than 10 Jy, whereas with SEST only 15 such masers were observed. The median values of $\log F_{\rm H_2O}$ are 1.78 and 1.45 for the H2O masers observed with SEST and Onsala, respectively. This corresponds to a difference by a factor of two in the flux density. The variability of H2O masers complicates the interpretation of these results. The flux densities of some sources may have changed by one or even two orders of magnitude after the catalogued measurements, and it is uncertain whether Fig. 4 represents a real correlation.

  
\begin{figure}
\vspace*{-1cm}
\centering
\psfig {file=fig4.eps,width=8.8cm,bbllx=50pt,bblly=80pt,bburx=550pt,bbury=750pt,angle=0}\end{figure} Figure 4: Number of observed sources and SiO detections as a function of the H2O maser peak flux density in Jy. Both Onsala and SEST survey objects are included

The H2O maser luminosity has been found to be related to the far-infrared luminosity of the associated IRAS Point Source Catalogue (PSC) objects (Wouterloot & Walmsley 1986). In their survey of a large sample of IRAS sources, Wouterloot et al. (1995) arrived at the conclusion that the observed maximum H2O maser luminosity at a certain FIR luminosity is proportional to $L_{\rm FIR}$ of the associated IRAS source (see their Fig. 8).

Most H2O masers in our sample are associated with IRAS point sources. According to the results of Wouterloot et al. (1995) the FIR flux density of an IRAS source could give an estimate for the upper limit of the integrated flux density of the associated H2O maser at any time. We have therefore plotted in Fig. 5a a histogram of SiO observations and detections as a function of the logarithm of the integrated FIR flux density ($F_{\rm FIR}$ [Wm-2]) for all IRAS point sources, which are located within a radius of $25^{\prime\prime}$ from the survey positions, and have "maser-like'' colours as determined by Wouterloot & Walmsley (1986) or have typical colours of UC HII regions as determined by Wood & Churchwell (1989). The integrated FIR flux density between 7 and 135 $\mu$m has been calculated by using the method of Emerson (1988). In Fig. 5b a similar histogram is presented for FIR luminosities ($L_{\rm FIR}$ [$L_\odot$]), calculated by using the distances given in Tables B.1 and B.2. Due to large overlap in the colour-colour diagrams of the associated IRAS sources and the observed spatial intermixing of H2O masers and UC HII regions we have not distinguished here between the two object categories. The total number of selected IRAS sources is 206, out of which 137 (67%) fullfill both colour criteria.

  
\begin{figure}
\vspace*{-1cm}
\centering
\psfig {file=fig5.eps,width=8.8cm,bbllx=50pt,bblly=50pt,bburx=550pt,bbury=850pt,angle=0}

\vspace*{4mm}\end{figure} Figure 5: Number of observed sources and SiO detections a) as a function of the integrated FIR flux density (Wm-2) and b) the FIR luminosity ($L_\odot$) of the associated IRAS point source. The point sources selected to the latter histogram have "maser-like'' or "UC HII-like'' colours (see text). The positional coincidence required is $25^{\prime\prime}$ or better. Both Onsala and SEST survey objects are included in these diagrams

One can see in Fig. 5a that the SiO detection rate is higher in the neighbourhood of IRAS point sources with large FIR flux densities, and exceeds $50\%$ in the range $-9.5 < \log{F_{\rm FIR}} <
-8.5$. According to Fig. 5b the detection rate is 40 percent or higher for sources with FIR luminosity higher than 4 solar luminosities. The correlation with the FIR luminosity is, however, less marked than in the case of the flux density. This is probably due to the fact that the SiO emission regions are relatively compact and their detection becomes more difficult with increasing distance. It should be noted furthermore that the uncertainties of the distance estimates may cause errors in the derived luminosities.

The minimum and maximum FIR flux density and luminosity are similar for the SEST and Onsala samples. However, the SEST sample contains more bright IRAS sources. The median values of $\log F_{\rm FIR}$ are -9.72 and -10.45 and the median values of $\log L_{\rm FIR}$ are 4.76 and 4.19 for the SEST and Onsala samples, respectively. The difference by a factor of 5 in the FIR flux density is particularly noteworthy. A closer look at the distribution of the IRAS sources shows that 54 percent of the IRAS sources with $\log
F_{\rm FIR} \gt -10$ are located in the galactic longitude range $300^\circ
\leq l \leq 0^\circ$, which contains 32 percent of the 206 selected IRAS sources.

The fact that the detection rate is higher towards bright IRAS sources suggests that the intensity of SiO emission is correlated with the thermal FIR emission from circumstellar dust around the associated young stellar object. On the other hand, the detection rate is higher for objects lying between the galactocentric distances 3 and 7 kpc (roughly sources in the galactic longitude range $300^\circ \leq l \leq 60^\circ$) than those located further away from the galactic centre. This region has a high molecular gas surface density and contains a large concentration of HII regions and embedded massive stars (e.g. Bronfman 1992; Blitz 1997). Due to a large number of sources in the corresponding part of the sky and the fact that we started from the brightest H2O masers and IRAS sources the final sample there contains a high fraction of probable SiO emission sources.

Is the higher detection rate for the sources belonging to the "molecular ring'' then a selection effect? In order to examine this we have plotted the SiO detection percentage as a function of the galactic longitude including only objects which are associated with bright IRAS point sources. Figure 6a represents sources with $\log F_{\rm FIR} \gt
-10.5$, whereas in Fig. 6b the detection rate is plotted for sources with $\log L_{\rm FIR}/L_\odot \gt 4$.The total number of sources falling within each $60^\circ$ wide interval is indicated in the lower left corner of the respective column. The errors have been estimated by assuming that the probability for detecting any specific number of sources in a certain longitude range is given by the binomial probability function. The histogram of the luminosity limited sample in Fig. 6a suggests that the detection rate is higher in the longitude range $300^\circ \leq l < 60^\circ$ than elsewhere, except perhaps the longitude range $240^\circ \leq l < 300^\circ$, where the relative error is rather large, however. The high detection rate in the latter interval is probably influenced by the fact that between $l=280^\circ$and $l=300^\circ$ we are looking along the Sagittarius-Carina arm (Georgelin & Georgelin 1976). The average detection rate within $300^\circ \leq l < 60^\circ$ for the luminosity limited sample is $61\pm6$%, whereas for the other two equal intervals of longitude the detections rates are $33\pm10$% ($180^\circ \leq l < 300^\circ$) and $23\pm7$% ($60^\circ \leq l < 180^\circ$). The corresponding averages for the flux limited sample are similar. It seems thus that the higher detection rate amongst the sources belonging to the "molecular ring'' cannot be solely explained by the fact that the selected target sources there are associated with brighter FIR sources.

  
\begin{figure}
\vspace*{-5mm}
\ \ \ \ \ \ 
\psfig {file=fig6.eps,width=8cm,bbllx=50pt,bblly=50pt,bburx=550pt,bbury=850pt,angle=0}

\vspace*{4mm}\end{figure} Figure 6: SiO detection percentages as a function of the galactic longitude a) for sources with $\log F_{\rm FIR} \gt
-10.5$ (Wm-2) and b) for sources with $\log L_{\rm FIR}/L_\odot \gt 4$. The number in the lower left of each column gives the total number of selected sources in the corresponding galactic longitude range

4.2 Line profiles

The distribution of the full widths above twice the RMS noise of the SiO(J=2-1) lines is presented as a histogram in Fig. 7. The velocity extent of the emission ranges from 2 to 60 kms-1, except for Ori KL where the line has a full width of 103 kms-1. The median value of the full width is 19 kms-1.

  
\begin{figure}
\centering
\psfig {file=fig7.eps,width=8.8cm,bbllx=70pt,bblly=70pt,bburx=510pt,bbury=790pt,angle=270}

~\end{figure} Figure 7: Number of detected sources as a function of the full width above two sigma of the SiO(J=2-1) line. Both Onsala and SEST detections are included in the data

In addition to their width the line shapes are described in Tables B.1 and B.2 by their symmetry or asymmetry with respect to the peak. We define an asymmetry parameter P as follows:


\begin{displaymath}
P \equiv \frac{V_{\rm peak} - V_{\rm cen}}{0.5 \,(V_{\rm max}-V_{\rm min})} \, ,\end{displaymath} (1)
where $V_{\rm cen} = (V_{\rm min} + V_{\rm max})/2$. The parameter P, which is twice the "normalized peak position or NPP'' of Palagi et al. (1993), can have values from -1 to +1. P=0 means that the line is symmetric. P = -1 and P=+1 correspond to cases where $V_{\rm
peak}=V_{\rm min}$ and $V_{\rm peak}=V_{\rm max}$, respectively.

The distributions of the asymmetry parameter P of the SiO(J=2-1) and SiO(J=3-2) spectra obtained at SEST are shown in Fig. 8. Only SEST observations were selected for this presentation, since they are better suited to analysis of the line shapes due to their higher S/N ratio and spectral resolution.

  
\begin{figure}
\vspace*{-2cm}
\centering
\psfig {file=fig8.eps,width=8.8cm,bbllx=50pt,bblly=80pt,bburx=550pt,bbury=900pt,angle=0}

\vspace*{+4mm}\end{figure} Figure 8: Distribution of the asymmetry parameter P for the SiO(J=2-1) a) and SiO(J=3-2) b) spectra obtained with the SEST. The value P=0 represents a symmetric line, a negative value corresponds to the case where the line peak is blueshifted with respect to the velocity centroid, and a posivite value indicates that the peak is redshifted with respect to the centroid

For both transitions the P-values are heavily concentrated close to zero. The mean values and the sample standard deviations of P for the J=2-1 and J=3-2 lines are $0.01\ \pm\ 0.26$ and $0.00\ \pm\ 0.28$. However, it is evident in the histograms and in the spectral figures of the Appendix B, that there is a number of highly asymmetric profiles with a steep rise on one side of the peak and a gradual fall on the other. The significance of full widths and the degree of asymmetry of the lines for the shock models are discussed in Sect. 5.4.

4.3 Peak velocities

For most sources detected in SiO, the velocities of the associated dense molecular cores as estimated from CS data are available. For this purpose we have used the surveys of Plume et al. (1992, 1997), Bronfmann et al. (1996), Juvela (1996) and Zinchenko et al. (1994, 1995). The distribution of the velocity differences between the SiO(J=2-1) line peaks and the CS line peak are shown in Fig. 9a. Figure 9b represents the corresponding separation with respect to the H2O maser emission peaks. Both SEST and Onsala data are included. The median velocity differences are indicated in the figure.

  
\begin{figure}
\psfig {file=fig9.eps,width=8.8cm,bbllx=70pt,bblly=60pt,bburx=520pt,bbury=750pt,angle=0}\end{figure} Figure 9: The distribution of velocity separation of the SiO(J=2-1) emission peaks with respect to a) the CS line peaks and b) the H2O maser line peaks in our sample

The SiO peak velocity is always close to the CS peak and thus the ambient cloud velocity. The average velocity separation (i.e. the absolute value of the difference) between the peaks, and its standard deviation are 1.02 and 1.06, respectively. The largest differences are towards the Onsala sources No. 150 (Jenness 21078+5211, -7.2 kms-1) and No. 162 (S140, $\rm +4.6~km~s^{-1}$).

The median SiO-H2O velocity difference is -0.6 km s-1. This is in consistence with the result of Wouterloot et al. (1995), where a mean separation of $-0.6 \pm 0.1$ km s-1 was found between H2O and CO line peak velocities for a much larger sample. The scatter in the SiO-H2O velocity difference is, however, markedly larger than for the pair SiO-CS. The average velocity separation between the H2O and SiO peaks and its standard deviation are 5.2 and 11.1, respectively. This reflects the fact that H2O maser components may have large velocities with respect to the ambient cloud. Three maser sources are highly blueshifted with respect to SiO. These objects are IRAS 09002-4412 (SEST No. 32, velocity difference -56 kms-1), NGC 6334 or GGD25 (SEST No. 131, -78 kms-1) and W51N (Onsala No. 104, -58 kms-1).

4.4 Line ratios

According to the shock chemistry model and SiO profile computations performed by Schilke et al. (1997), the integrated intensity ratio J=3-2/J=2-1 depends on the pre-shock density. As indicated in their Fig. 6, the J=2-1 line is stronger than J=3-2 at low densities but weaker at high densities. The intensities are roughly equal at $n_{\rm H} = 10^5$ cm-3.

The distribution of the integrated antenna temperature J=3-2/J=2-1 in our SEST observations is shown in Fig. 10. The median of the distribution is 1.1. The antenna temperature ratio can be converted to the brightness temperature ratio taking the different beam sizes and beam efficiences at the transition frequencies into account. The formula needed for this conversion is given in Anglada et al. (1996), Eq. (A2). The antenna and beam efficiencies and beam widths for the SEST are given in Table 1. For a circular source with uniform surface brightness, the conversion factor between the $T_{\rm B}(3-2)/T_{\rm B}(2-1)$ ratio and the corresponding $T_{\rm A}^*$ ratio ranges from 0.54 (for very small sources) to 1.1 (for extended sources). If the source size is smaller than $1^\prime$ the conversion factor is less than 0.75. According to the existing SiO maps sources are typically small and the conversion factor is probably close to the lower limit 0.54. In the light of the calculations of Schilke et al. (1997) the observed J=3-2/J=2-1 ratios suggest that the typical gas densities in the studied regions are moderate ($\leq 10^5$ cm-3).

Without maps and observations of rare isotopomers this cannot confirmed, however. In LTE the brightness temperature ratio $T_{\rm B}(3-2)/T_{\rm B}(2-1)$approaches 2.25 at high values of $T_{\rm ex}$ in the optically thin case (see the next subsection). This is the absolute maximum since the ratio decreases along with the optical thickness and approaches unity at very high values of the SiO column density. The integrated intensity ratios are likely to follow the optically thin case even though the optical thickness is probably high at the line peaks. Depending on the source sizes the few cases with J=3-2/J=2-1 ratios close to 2 may represent high values of $T_{\rm ex}$ and thus high densities.

  
\begin{figure}
\psfig {file=fig10.eps,width=8.8cm,bbllx=50pt,bblly=80pt,bburx=550pt,bbury=800pt,angle=0}\end{figure} Figure 10: The integrated intensity ratio of the SiO (J=3-2) and (J=2-1) lines

4.5 Excitation temperatures

In order to estimate the excitation temperatures of the SiO lines, we measured with SEST the J=2-1 and J=3-2 transitions of both 28SiO and 29SiO towards three strong sources. These are Ori KL (No. 3 in Table B.1.), OH328.81+0.63 (No. 91) and G351.77-0.54 (No. 135). The obtained spectra are shown in Fig. 11.

The v=0,J=2-1 transition in Ori KL is masing, which is clearly visible in the 29SiO spectrum. The maser components, arising either from an expanding shell (see e.g. Chandler & De Pree 1995) or a rotating disk (Plambeck et al. 1990) around IRc2, are naturally present also in the normal isotope spectrum, but buried in the thermal emission. The maser components of the 28SiO(J=2-1) spectrum can be traced by dividing the purely thermal 28SiO(J=3-2) spectrum by the former, which brings out two deep dips at the same velocities where also the 29SiO peaks are located. This is caused by the fact that the brightness temperature ratio SiO(J=2-1)/(J=3-2) lines increases sharply at velocities corresponding to the regions where the population inversion between the levels J=2 and J=1 occurs. The v=0 maser components are at -6.8 and 16.2 km s-1 i.e. at slightly larger offsets from the molecular cloud velocity than the v=1 features.

  
\begin{figure*}
\psfig {file=fig11.eps,width=18.0cm,bbllx=50pt,bblly=40pt,bburx=550pt,bbury=800pt,angle=270}\end{figure*} Figure 11: The v=0,J=3-2 and v=0,J=2-1 lines of 28SiO and 29SiO towards Ori KL, OH328.81+0.63 and G351.77-0.54. The weaker 29SiO spectra are multiplied by 2

In LTE the optical thickness ratio of the transitions $3 \rightarrow 2$and $2 \rightarrow 1$, as a function of the excitation temperature $T_{\rm ex}$, is approximately
\begin{displaymath}
\frac{\tau_{3 \rightarrow 2}}{\tau_{2 \rightarrow 1}} \appro...
 ...e}^{3 E_1/T_{\rm ex}} - 1}{{\rm e}^{2 E_1/T_{\rm ex}} - 1} \, ,\end{displaymath} (2)
where $E_1 \equiv h \nu_{10}/k$ equals 2.08 K for the SiO molecule in the vibrational ground state. The optical thickness ratio $\tau(3-2)/\tau(2-1)$for SiO exceeds unity when $T_{\rm ex}$ is greater than about 7 K, and the upper limit of the ratio when $T_{\rm ex}$ approaches infinity is (3/2)2 = 2.25. The ratios at the line peaks for Ori KL, OH328.81+0.63 and G351.77-0.54 are 1.6, 0.9 and 1.0, respectively. The corresponding values of $T_{\rm ex}$ from the LTE assumption are 18, 6 and 7 K.

For the thermal sources the optical thickness ratios do not change considerably over the velocity ranges where the signal to noise ratio is reasonable, i.e. $-55 \rightarrow$ -35 km s-1 and $-15 \rightarrow 10$km s-1 for OH328.81+0.63 and G351.77-0.54, respectively, suggesting that the excitation temperatures are equally low in the high-velocity gas.

The derived excitation temperature (18 K) towards Ori KL is much lower than the kinetic temperature of the SiO emission region ($\sim 200$ K, see. e.g. Deguchi & Nguyen-Quang-Rieu 1983). The derived excitation temperatures (6 and 7 K) are very likely to be lower than the kinetic temperatures also in the two other sources.

Acord et al. (1997) derived, from NH3 and CO observations, a kinetic temparature of 100 K for the outflowing gas associated with the ultracompact HII region and outflow source G5.89-0.39 (close to the H2O maser W28 A2(2), No. 144 in Table B.2). They also observed several SiO transitions towards this source and used statistical equilibrium calculations for determining other physical parameters of the outflowing gas. The rotational temperature of SiO was found to be about 12 K, i.e. clearly subthermal.

The low values of $T_{\rm ex}$ derived for the mentioned four sources suggest that the average densities of the SiO emission regions there are not particularly high. They probably remain below the critical density of the SiO(v=0,J=3-2) line, $\sim 3 \, 10^6$ cm-3 at 100 K (Turner et al. 1992), and are thus clearly lower than the densities required for H2O maser excitation, i.e. $n_{\rm H_2} \sim 10^9$ cm-3.


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