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<!-- DOI: 10.1051/0004-6361/201014590 -->

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

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<tr><td><!-- init Label --><A NAME="RMvsstop"></A><!-- end Label--><A NAME="973"></A><A NAME="figure783" HREF="img33.png"><IMG SRC="Timg33.png" ALT="\begin{figure}
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<td class="img-txt"><span class="bold">Figure 2:</span><p>
The H<sub>2</sub> mass fraction as a function of the stopping criterion.
The vertical line indicates where <IMG SRC="img2.png" ALT="$T_{\rm e}$" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="16">
reaches 4000&nbsp;K.
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<td class="img-txt"><span class="bold">Figure 3:</span><p>
The standard model of AG04 recreated with Cloudy.
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<td class="img-txt"><span class="bold">Figure 4:</span><p>
Same as Fig.&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#RMvsstop">2</a>, but for the standard4 model.
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<td class="img-txt"><span class="bold">Figure 5:</span><p>
Same as Fig.&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#standmod">3</a>, but for the standard4 model.
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<tr><td><!-- init Label --><A NAME="h2:timescales"></A><!-- end Label--><A NAME="977"></A><A NAME="figure806" HREF="img37.png"><IMG SRC="Timg37.png" ALT="\begin{figure}
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<td class="img-txt"><span class="bold">Figure 6:</span><p>
The H<sub>2</sub> formation and destruction timescales (solid and dotted
lines, respectively) for knots with a central density of 10<sup>5</sup>, 10<sup>6</sup>, and 10<sup>7</sup>&nbsp;cm<sup>-3</sup> just outside the ionized region.
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<p></p><p></p><h2 class="sec"><a name="SECTION00070000000000000000"></a>
<A NAME="reduction"></A>
Appendix A: Data reduction
</h2>

<p>NGC 6720 was observed by PACS in scan map mode (one scan and one cross scan), obtaining maps in the blue (70&nbsp;<IMG SRC="img1.png" ALT="$\mu $" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="11">m) and red (160&nbsp;<IMG SRC="img1.png" ALT="$\mu $" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="11">m) bands. The data were processed with the <i>Herschel</i> Interactive data Processing Environment (HIPE, <A NAME="aaref22"></A><a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#Ott10">Ott  2010</a>),
following the recommended pipeline for these data. This will be
explained in detail in later papers, but a few deviations and
customizations are noted here. The WCS has an offset of a few
arcseconds that was corrected for the comparison of the PACS map to
others (using known sources in the field). We used the version&nbsp;3
flatfield calibration. The signals were converted to&nbsp;Jy using the
version&nbsp;5 calibration table. We did not remove the cross-talk or
corrected for response drifts. Cross-talk correction is not part of the
pipeline at present. Response drifts are unlikely to be a problem for
our observations: we find no drift in the calibration source signals of
more than&nbsp;1.5% over the duration of the observations. Removal of
the glitches (cosmic&nbsp;rays) was done in two stages: first from the
regions around our source by filtering along the time-dimension, and
then from the source itself working this time on the image plane.
Cleaning the maps of the 1/f&nbsp;noise (the name refers to the type of
power spectral density the noise has) was done using a high-pass filter
method. Here a filter passes over the data as a function of time,
subtracting the median of the data over a specified time span (filter
width). This allows the high noise frequencies to pass and attenuates
the lower frequencies. Considering that moving forward in time means
moving along a spatial direction as the instrument is scanning over
the source, it&nbsp;is clear that setting a low value for the filter
width will rapidly remove varying noise but can have the consequence of
removing extended emission. We processed the data with a variety of
filter widths, but for our source it made little difference to the
photometry or morphology. Also worth noting is that the high-pass
filter creates artificial negative ``sidelobes''
around strong sources. To&nbsp;deal with this the source was masked out
before running the high-pass filter. Finally the scan and cross scan
frames were combined and turned into&nbsp;a&nbsp;map.
</p><p>Prior to making the maps presented in this paper the background
sources were removed with the HIPE sourceExtractorDaophot task. Slight
WCS offsets for the PACS and SPIRE maps were corrected, using
background source coordinates measured in the Calar Alto image. The
pixel sizes and beam widths are given in&nbsp;Table&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#phot">B.1</a>.

</p><p>We custom-processed the raw <i>Spitzer</i> data obtained from
the archive using both the GeRT and Mosaicker software to remove some
obvious anomalies apparent in the pipeline-processed images by
following the procedure explained by <A NAME="aaref29"></A><a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#Ue06">Ueta (2006)</a>.

</p><p>We did the observations of NGC 6720 in the H<sub>2</sub>&nbsp;band
by alternating object and sky exposures. We reduced the data in the
PixInsight Core package using the acquired bias, dark, flatfield and
sky frames. Special care was taken to avoid artifacts in the object
frames caused by the presence of stars in the sky frames.
A&nbsp;percentile clipping integration was done on the sky frames,
grouping them in groups of 5&nbsp;images. By&nbsp;fitting the average
signal of the (already bias, dark and flatfield corrected) sky frames,
a&nbsp;tight rejection of outliers was possible, allowing the removal
of the stars in the images. Then the resulting sky frame was subtracted
from the object frame acquired in the
middle of the five sky frames. We corrected the residual background
gradients due to sky variation by subtracting a sky background model
built with the DynamicBackgroundExtraction module of PixInsight.
Finally this image was astrometrically calibrated using the
astrometry.net package (<A NAME="aaref13"></A><a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#La09">Lang et&nbsp;al.  2010</a>).

</p><p></p><h2 class="sec"><a name="SECTION00080000000000000000"></a>
<A NAME="photometry"></A>Appendix B: Photometry
</h2>

<p><A NAME="phot"></A><p class="inset-old"><a href="/articles/aa/full_html/2010/10/aa14590-10/tableB.1.html"><span class="bold">Table B.1:</span></a>&#160;&#160;
Aperture photometry of NGC 6720 in various photometric bands.</p> 

<p>To measure the fluxes from the PACS, SPIRE and <i>Spitzer</i> maps we used an elliptical aperture around NGC&nbsp;6720. The measured values are given in Table&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#phot">B.1</a>. The PACS data were already in Jy/pix, the SPIRE data were converted from Jy/beam to Jy/pix using the conversion 
<!-- MATH: $\pi({\rm beam/pixel})^2/(4\ln2)$ -->
<IMG SRC="img55.png" ALT="$\pi({\rm beam/pixel})^2/(4\ln2)$" ALIGN="MIDDLE" BORDER="0" HEIGHT="30" WIDTH="135">
where the pixel and beam sizes are listed in Table&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#phot">B.1</a>.
The measured fluxes were also multiplied by factors provided by the
SPIRE team as the calibration tables did not yet include these<A NAME="tex2html13" HREF="#foot840"><sup><IMG ALT="[*]" SRC="/icons/foot_motif.png" align="bottom" BORDER="1"></sup></A>. The <i>Spitzer</i>
data were in MJy/sr and were converted to Jy/pix via the conversion
given in the MIPS instrument handbook (Sect.&nbsp;4.3).
No&nbsp;additional corrections were applied (e.g. color corrections).
Uncertainties are quoted in Table&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#phot">B.1</a>.
Calibration
uncertainties were taken from the respective instrument guides or
release notes. Measurement errors are difficult to calculate,
as&nbsp;for these (bolometer) instruments the Poissonian errors are not
easily obtained. We combined the contribution of the sky noise, the
values in the error arrays which the PACS and SPIRE pipelines create,
and the variation in map fluxes that different reasonable pipeline
parameter variations gave. For&nbsp;the <i>Spitzer</i> fluxes no measurement uncertainties were calculated.

</p><p>As the beam size and the pixel scales on the maps are all different we
measured all the flux that could be seen from the source down to the
sky level, independently for each map. The aperture sizes used are
included in&nbsp;Table&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#phot">B.1</a>.

</p><p></p><h2 class="sec"><a name="SECTION00090000000000000000"></a>
<A NAME="model"></A>Appendix C: The photoionization model
</h2>

<p>We used the method described in <A NAME="aaref30"></A><a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#vH99">van Hoof &amp; Van de Steene (1999)</a>
to create an optimized photoionization model of NGC&nbsp;6720 using a
prerelease of version&nbsp;C10.00 of the photoionization code Cloudy
(revision&nbsp;3862). The method was slightly modified in that we used
H-Ni&nbsp;model atmospheres from <A NAME="aaref25"></A><a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#Ra03">Rauch (2003)</a>. As&nbsp;input we used the UV and optical spectrum listed in <A NAME="aaref14"></A><a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#Liu04">Liu et&nbsp;al. (2004)</a>.
We rejected the SWS&nbsp;spectrum as it turned out that the aperture
was mainly pointed at the central ``cavity'' and was therefore strongly
biased towards the high excitation region of the nebula. This made
aperture correction factors highly dependent on the ionization stage
and hence very uncertain. We did use a re-reduced
version of the LWS&nbsp;spectrum of NGC&nbsp;6720, adopting the
aperture correction factor listed in <a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#Liu04">Liu et&nbsp;al. (2004)</a>. The [O&nbsp; <small>I</small>]&nbsp;lines
were excluded from the modeling because they were fitted very badly.
A&nbsp;plausible explanation is that these lines are predominantly
formed in the knots. We added two dust continuum flux measurements from
the LWS&nbsp;spectrum at&nbsp;43 and 115&nbsp;<IMG SRC="img1.png" ALT="$\mu $" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="11">m of 4&nbsp;<IMG SRC="img24.png" ALT="$\times$" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="12">&nbsp;10<sup>-18</sup> and 5&nbsp;<IMG SRC="img24.png" ALT="$\times$" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="12">
10<sup>-19</sup>&nbsp;W&nbsp;cm<sup>-2</sup>&nbsp;<IMG SRC="img1.png" ALT="$\mu $" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="11">m<sup>-1</sup>
respectively (aperture correction factors have not yet been applied to
these values). We also used two radio continuum flux densities
at&nbsp;4850 and 1400&nbsp;MHz of&nbsp;360 and 440&nbsp;mJy
respectively, which are averages of the data collected by <A NAME="aaref32"></A><a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#Vo09">Vollmer et&nbsp;al. (2010)</a>. For the angular diameter we used 76
<!-- MATH: $^{\prime\prime}$ -->
<IMG SRC="img6.png" ALT="$^{\prime\prime}$" align="bottom" BORDER="0" HEIGHT="14" WIDTH="10">
(<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#Liu04">Liu et&nbsp;al.  2004</a>). We
adopted a distance of 740&nbsp;pc (<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#OD09">O'Dell et&nbsp;al.  2009</a>).
The model was stopped when the electron temperature dropped below
4000&nbsp;K. The resulting optimized model has the parameters listed in
Table&nbsp;<a href="/articles/aa/full_html/2010/10/aa14590-10/aa14590-10.html#model:par">1</a>. Most symbols have their usual meaning. <IMG SRC="img17.png" ALT="$\Gamma$" align="bottom" BORDER="0" HEIGHT="14" WIDTH="12">&nbsp;denotes the dust-to-gas mass ratio and&nbsp;<IMG SRC="img10.png" ALT="$\epsilon$" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="9">
the logarithmic abundance of an element (<IMG SRC="img10.png" ALT="$\epsilon$" ALIGN="MIDDLE" BORDER="0" HEIGHT="26" WIDTH="9">(H)&nbsp;<IMG SRC="img56.png" ALT="$\equiv$" align="bottom" BORDER="0" HEIGHT="14" WIDTH="12">&nbsp;12.00).
The
electron temperature and density are averaged over the ionized nebula.
We will refer to this model as the standard Cloudy model of
NGC&nbsp;6720.
</p><p></p>
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