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<!-- DOI: 10.1051/0004-6361/200913919 -->

<h2 class="sec">Online Material</h2>

<p></p><h2 class="sec"><a name="SECTION000110000000000000000"></a>
<A NAME="chisqplots"></A>
Appendix A: <IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surfaces for RADEX fits
</h2>

<p>Figures&nbsp;<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#fig:NA">A.1</a>-<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#fig:SD">A.8</a> show the <IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surfaces from the
non-LTE analysis of the line integrated intensity ratios for each of the
positions studied.  The <IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
has been calculated using
Eq.&nbsp;(<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#eq:chisq">A.1</a>), where 
<!-- MATH: $I_{(J_{\rm up}-J_{\rm low})}^{{\rm obs}}$ -->
<IMG SRC="img78.png" ALT="$I_{(J_{\rm up}-J_{\rm low})}^{{\rm obs}}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="49">
is the
observed integrated intensity of the transition between 
<!-- MATH: $J_{\rm up}$ -->
<IMG SRC="img79.png" ALT="$J_{\rm up}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="21">
and

<!-- MATH: $J_{\rm low}$ -->
<IMG SRC="img80.png" ALT="$J_{\rm low}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="25">,
<IMG SRC="img81.png" ALT="$\Delta$" align="bottom" BORDER="0" HEIGHT="14" WIDTH="13">(<i>x</i>) is the uncertainty on the quantity <i>x</i> and, finally,

<!-- MATH: $I_{(J_{\rm up}-J_{\rm low})}^{{\rm radex}}$ -->
<IMG SRC="img82.png" ALT="$I_{(J_{\rm up}-J_{\rm low})}^{{\rm radex}}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="49">
is the integrated intensity for each
transition as modelled by RADEX, for each combination of temperature and gas
column density

</p><p></p><DIV ALIGN="CENTER"><A NAME="eq:chisq"></A>
<!-- MATH: \begin{eqnarray}
\chi^{2} &=& \left(\frac{I_{(1-0)}^{{\rm obs}}/I_{(2-1)}^{{\rm obs}} - I_{(1-0)}^{{\rm radex}}/I_{(2-1)}^{{\rm radex}}}{\Delta(I_{(1-0)}^{{\rm obs}}/I_{(2-1)}^{{\rm obs}})}\right)^{2} \nonumber\\&&+ \left(\frac{I_{(1-0)}^{{\rm obs}}/I_{(3-2)}^{{\rm obs}} - I_{(1-0)}^{{\rm radex}}/I_{(3-2)}^{{\rm radex}}} {\Delta(I_{(1-0)}^{{\rm obs}}/I_{(3-2)}^{{\rm obs}})}\right)^{2}\nonumber\\&&+
\left(\frac{I_{(1-0)}^{{\rm obs}} - I_{(1-0)}^{{\rm radex}}}{\Delta(I_{(1-0)}^{{\rm obs}})}\right)^{2}\cdot
\end{eqnarray} -->
<TABLE ALIGN="CENTER" cellpadding="0" WIDTH="100%">
<tbody><tr VALIGN="MIDDLE"><td ALIGN="RIGHT" nowrap="nowrap">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<IMG SRC="img83.png" ALT="$\displaystyle \chi^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="35" WIDTH="18">
</td>
<td ALIGN="CENTER" nowrap="nowrap">=
</td>
<td ALIGN="LEFT" nowrap="nowrap"><IMG SRC="img84.png" ALT="$\displaystyle \left(\frac{I_{(1-0)}^{{\rm obs}}/I_{(2-1)}^{{\rm obs}} - I_{(1-0...
...^{{\rm radex}}}{\Delta(I_{(1-0)}^{{\rm obs}}/I_{(2-1)}^{{\rm obs}})}\right)^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="68" WIDTH="180">
</td>
<td ALIGN="RIGHT" WIDTH="10">
&nbsp;
</td>
</tr>
<tr VALIGN="MIDDLE"><td ALIGN="RIGHT" nowrap="nowrap">&nbsp;
</td>
<td>&nbsp;
</td>
<td ALIGN="LEFT" nowrap="nowrap"><IMG SRC="img85.png" ALT="$\displaystyle + \left(\frac{I_{(1-0)}^{{\rm obs}}/I_{(3-2)}^{{\rm obs}} - I_{(1...
...{{\rm radex}}} {\Delta(I_{(1-0)}^{{\rm obs}}/I_{(3-2)}^{{\rm obs}})}\right)^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="68" WIDTH="192">
</td>
<td ALIGN="RIGHT" WIDTH="10">
&nbsp;
</td>
</tr>
<tr VALIGN="MIDDLE"><td ALIGN="RIGHT" nowrap="nowrap">&nbsp;
</td>
<td>&nbsp;
</td>
<td ALIGN="LEFT" nowrap="nowrap"><IMG SRC="img86.png" ALT="$\displaystyle +
\left(\frac{I_{(1-0)}^{{\rm obs}} - I_{(1-0)}^{{\rm radex}}}{\Delta(I_{(1-0)}^{{\rm obs}})}\right)^{2}\cdot$" ALIGN="MIDDLE" BORDER="0" HEIGHT="68" WIDTH="123">
</td>
<td ALIGN="RIGHT" WIDTH="10">
(A.1)
</td>
</tr>
</table></div><br clear="all"><p></p>
<p>For each case, the <IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
is plotted as a function of the RADEX output
temperature and gas column density. Given the use of 3 quantities in the fit,
we consider 
<!-- MATH: $\chi^{2}<3$ -->
<IMG SRC="img87.png" ALT="$\chi^{2}&lt;3$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="41">,
i.e. the reduced-
<!-- MATH: $\chi^{2}<1$ -->
<IMG SRC="img88.png" ALT="$\chi^{2}&lt;1$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="40">
a good fit. All
figures have contours at 
<!-- MATH: $\chi^{2}=1$ -->
<IMG SRC="img89.png" ALT="$\chi^{2}=1$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="41">,
2 and 3 with the exception of ND
(Fig.&nbsp;<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#fig:ND">A.4</a>) and SD (Fig.&nbsp;<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#fig:SD">A.8</a>).
<br>
<br>
</p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:NA"></A><!-- end Label--><A NAME="2069"></A><A NAME="figure1705" HREF="img90.png"><IMG SRC="Timg90.png" ALT="\begin{figure}
\par\includegraphics[scale=.37,angle=-90]{13919fga1.eps}
\end{figure}" HEIGHT="68" WIDTH="78"></A><!-- HTML Figure number: 16 -->
</td>
<td class="img-txt"><span class="bold">Figure A.1:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surface for the integrated intensity ratios at position NA.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=16&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:NB"></A><!-- end Label--><A NAME="2070"></A><A NAME="figure1711" HREF="img91.png"><IMG SRC="Timg91.png" ALT="\begin{figure}
\par\includegraphics[scale=.37,angle=-90]{13919fga2.eps}
\end{figure}" HEIGHT="68" WIDTH="79"></A><!-- HTML Figure number: 17 -->
</td>
<td class="img-txt"><span class="bold">Figure A.2:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surface for the integrated intensity ratios at position NB.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=17&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:NC"></A><!-- end Label--><A NAME="2071"></A><A NAME="figure1717" HREF="img92.png"><IMG SRC="Timg92.png" ALT="\begin{figure}
\par\includegraphics[scale=.37,angle=-90]{13919fga3.eps}
\end{figure}" HEIGHT="68" WIDTH="78"></A><!-- HTML Figure number: 18 -->
</td>
<td class="img-txt"><span class="bold">Figure A.3:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surface for the integrated intensity ratios at position NC.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=18&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:ND"></A><!-- end Label--><A NAME="2072"></A><A NAME="figure1723" HREF="img93.png"><IMG SRC="Timg93.png" ALT="\begin{figure}
\par\includegraphics[scale=.37,angle=-90]{13919fga4.eps}
\end{figure}" HEIGHT="68" WIDTH="79"></A><!-- HTML Figure number: 19 -->
</td>
<td class="img-txt"><span class="bold">Figure A.4:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surface for the integrated intensity ratios at position ND. Contour at 25.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=19&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:SA"></A><!-- end Label--><A NAME="2074"></A><A NAME="figure1729" HREF="img94.png"><IMG SRC="Timg94.png" ALT="\begin{figure}
\mbox{\includegraphics[scale=.37,angle=-90]{13919fga5a.eps} \h...
...egraphics[scale=.37,angle=-90]{13919fga5b.eps} }
\hfill
\hfill
\end{figure}" HEIGHT="68" WIDTH="170"></A><!-- HTML Figure number: 20 -->
</td>
<td class="img-txt"><span class="bold">Figure A.5:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surfaces for the integrated intensity ratios at
      position SA: SA1 (LVC) on the <i> left</i>, and SA2 (HVC) on the <i> right</i>.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=20&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:SB"></A><!-- end Label--><A NAME="2076"></A><A NAME="figure1739" HREF="img95.png"><IMG SRC="Timg95.png" ALT="\begin{figure}
\mbox{\includegraphics[scale=.37,angle=-90]{13919fga6a.eps} \h...
...udegraphics[scale=.37,angle=-90]{13919fga6b.eps} }
\hfill
\hfill\end{figure}" HEIGHT="68" WIDTH="171"></A><!-- HTML Figure number: 21 -->
</td>
<td class="img-txt"><span class="bold">Figure A.6:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surface for the integrated intensity ratios at position SB: SB1
(LVC) on the <i> left</i>, and SB2 (HVC) on the <i> right</i>.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=21&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:SC"></A><!-- end Label--><A NAME="2078"></A><A NAME="figure1749" HREF="img96.png"><IMG SRC="Timg96.png" ALT="\begin{figure}
\mbox{\includegraphics[scale=.37,angle=-90]{13919fga7a.eps} \h...
...degraphics[scale=.37,angle=-90]{13919fga7b.eps} }
\hfill
\hfill
\end{figure}" HEIGHT="68" WIDTH="170"></A><!-- HTML Figure number: 22 -->
</td>
<td class="img-txt"><span class="bold">Figure A.7:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surface for the integrated intensity ratios at
      position SC: SC1 (LVC) on the <i>left</i> and SC2 (HVC) on the <i>right</i>.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=22&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><div class="inset-old">
<table>
<tr><td><!-- init Label --><A NAME="fig:SD"></A><!-- end Label--><A NAME="2080"></A><A NAME="figure1759" HREF="img97.png"><IMG SRC="Timg97.png" ALT="\begin{figure}
\mbox{\includegraphics[scale=.38,angle=-90]{13919fga8a.eps} \h...
...degraphics[scale=.38,angle=-90]{13919fga8b.eps} }
\hfill
\hfill\end{figure}" HEIGHT="69" WIDTH="174"></A><!-- HTML Figure number: 23 -->
</td>
<td class="img-txt"><span class="bold">Figure A.8:</span><p>
<IMG SRC="img10.png" ALT="$\chi ^{2}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="16">
surface for the integrated intensity ratio at position
SD: SD1 (LVC) on the <i> left</i>, and SD2 (HVC) on the <i> right</i>. Note the different colour scale for SC2. Contours are 6 for SD1 and 18 for SD2.
</td>
</tr><tr><td colspan="2"><a href="http://dexter.edpsciences.org/applet.php?pdf_id=23&DOI=10.1051/0004-6361/200913919" target="DEXTER">Open with DEXTER</a></td></tr>

</table></div>
<p></p><h2 class="sec"><a name="SECTION000120000000000000000"></a>
<A NAME="intensities"></A>Appendix B: C<sup>18</sup>O intensities  and abundances
</h2>

<p>Table&nbsp;<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#tab:intens">B.1</a> presents the best fit integrated intensities from the non-LTE (RADEX) modelling (Appendix&nbsp;<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#chisqplots">A</a>) , together with the observed values, and the implied C<sup>18</sup>O abundances.
<A NAME="tab:intens"></A><p class="inset-old"><a href="/articles/aa/full_html/2010/11/aa13919-09/tableB.1.html"><span class="bold">Table B.1:</span></a>&#160;&#160;
Modelled integrated intensities and resulting abundances.</p>
<p>For positions ND, SB, SC and SD, the H<sub>2</sub> column densities derived from the
dust and used to estimate the abundance of C<sup>18</sup>O were calculated using a
dust temperature of 10&nbsp;K.  Assuming a temperature of 15&nbsp;K for all 4 positions
(ND, SB, SC and SD) would reduce the H<sub>2</sub> column densities by a factor of
2.1, representing an equivalent rise of the fractal abundance of C<sup>18</sup>O by
the same amount.

</p><p>The derived C<sup>18</sup>O fractional abundance (which is averaged along the line
of sight) implies a depletion of C<sup>18</sup>O of between a factor of 1.4 (for NC)
and 4.3 (for SC), with an average of 2.5 compared to the abundance of

<!-- MATH: $1.7\times10^{-7}$ -->
<IMG SRC="img99.png" ALT="$1.7\times10^{-7}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="62">
in dark clouds (<a href="/articles/aa/full_html/2010/11/aa13919-09/aa13919-09.html#1982ApJ...262..590F">Frerking et&nbsp;al.  1982</a>).  Given that the
ratio between C<sup>17</sup>O and C<sup>18</sup>O has shown these two species to be
optically thin, with an intensity ratio of <IMG SRC="img13.png" ALT="$\sim$" align="bottom" BORDER="0" HEIGHT="14" WIDTH="13">3.5, a factor 2.5 depletion
of C<sup>18</sup>O implies the same depletion factor for C<sup>17</sup>O.

</p><p></p><p></p>
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