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	Figure 2: The H2 mass fraction as a function of the stopping criterion. The vertical line indicates where reaches 4000 K.
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	Figure 3: The standard model of AG04 recreated with Cloudy.
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	Figure 4: Same as Fig. 2, but for the standard4 model.
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	Figure 5: Same as Fig. 3, but for the standard4 model.
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	Figure 6: The H2 formation and destruction timescales (solid and dotted lines, respectively) for knots with a central density of 105, 106, and 107 cm-3 just outside the ionized region.
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Appendix A: Data reduction

NGC 6720 was observed by PACS in scan map mode (one scan and one cross scan), obtaining maps in the blue (70 m) and red (160 m) bands. The data were processed with the Herschel Interactive data Processing Environment (HIPE, Ott 2010), 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 3 flatfield calibration. The signals were converted to Jy using the version 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 1.5% over the duration of the observations. Removal of the glitches (cosmic 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 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 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 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 a map.

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 Table B.1.

We custom-processed the raw Spitzer 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 Ueta (2006).

We did the observations of NGC 6720 in the H₂ 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 percentile clipping integration was done on the sky frames, grouping them in groups of 5 images. By fitting the average signal of the (already bias, dark and flatfield corrected) sky frames, a 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 (Lang et al. 2010).

Appendix B: Photometry

Table B.1:   Aperture photometry of NGC 6720 in various photometric bands.

To measure the fluxes from the PACS, SPIRE and Spitzer maps we used an elliptical aperture around NGC 6720. The measured values are given in Table B.1. The PACS data were already in Jy/pix, the SPIRE data were converted from Jy/beam to Jy/pix using the conversion where the pixel and beam sizes are listed in Table B.1. The measured fluxes were also multiplied by factors provided by the SPIRE team as the calibration tables did not yet include these. The Spitzer data were in MJy/sr and were converted to Jy/pix via the conversion given in the MIPS instrument handbook (Sect. 4.3). No additional corrections were applied (e.g. color corrections). Uncertainties are quoted in Table B.1. Calibration uncertainties were taken from the respective instrument guides or release notes. Measurement errors are difficult to calculate, as 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 the Spitzer fluxes no measurement uncertainties were calculated.

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 Table B.1.

Appendix C: The photoionization model

We used the method described in van Hoof & Van de Steene (1999) to create an optimized photoionization model of NGC 6720 using a prerelease of version C10.00 of the photoionization code Cloudy (revision 3862). The method was slightly modified in that we used H-Ni model atmospheres from Rauch (2003). As input we used the UV and optical spectrum listed in Liu et al. (2004). We rejected the SWS 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 spectrum of NGC 6720, adopting the aperture correction factor listed in Liu et al. (2004). The [O  I] lines were excluded from the modeling because they were fitted very badly. A plausible explanation is that these lines are predominantly formed in the knots. We added two dust continuum flux measurements from the LWS spectrum at 43 and 115 m of 4  10^-18 and 5  10^-19 W cm^-2 m^-1 respectively (aperture correction factors have not yet been applied to these values). We also used two radio continuum flux densities at 4850 and 1400 MHz of 360 and 440 mJy respectively, which are averages of the data collected by Vollmer et al. (2010). For the angular diameter we used 76 (Liu et al. 2004). We adopted a distance of 740 pc (O'Dell et al. 2009). The model was stopped when the electron temperature dropped below 4000 K. The resulting optimized model has the parameters listed in Table 1. Most symbols have their usual meaning.  denotes the dust-to-gas mass ratio and  the logarithmic abundance of an element ((H)  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 6720.