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Acknowledgements

HIFI has been designed and built by a consortium of institutes and university departments from across Europe, Canada and the United States under the leadership of SRON Netherlands Institute for Space Research, Groningen, The Netherlands and with major contributions from Germany, France and the US. Consortium members are: Canada: CSA, U.Waterloo; France: CESR, LAB, LERMA, IRAM; Germany: KOSMA, MPIfR, MPS; Ireland, NUI Maynooth; Italy: ASI, IFSI-INAF, Osservatorio Astrofisico di Arcetri- INAF; Netherlands: SRON, TUD; Poland: CAMK, CBK; Spain: Observatorio Astronomico Nacional (IGN), Centro de Astrobiologia (CSIC-INTA). Sweden: Chalmers University of Technology - MC2, RSS & GARD; Onsala Space Observatory; Swedish National Space Board, Stockholm University - Stockholm Observatory; Switzerland: ETH Zurich, FHNW; USA: Caltech, JPL, NHSC. The work on star formation at ETH Zurich is partially funded by the Swiss National Science Foundation (grant nr. 200020-113556). This program is made possible thanks to the Swiss HIFI guaranteed time program. This work was supported by the German Deutsche Forschungsgemeinschaft, DFG project number Os 177/1-1. We thank the members of the Herschel key project ``Galactic Cold Cores: A Herschel survey of the source populations revealed by Planck'' lead by M. Juvela (KPOT_mjuvela) for providing us with the results of the SPIRE 250 m mapping and fruitful discussions. We would also like to acknowledge the use of the JCMT CO(3-2) archival data (PI M. Thompson, M08BU15). A portion of this research was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space administration. We would like to thank an anonymous referee for constructive comments.

Appendix A: Comparison of line profiles taken with different beams

The different lines discussed here were measured at various telescopes and at different frequencies, so that they all represent somewhat different spatial resolutions. To allow a comparison in terms of a physical interpretation, they have to be translated to a common resolution, so that they stem from the same area on the sky. As a reference, we use , the resolution of the KOSMA observations in the 3-2 transition of the CO isotopes. In principle, all data taken at a finer resolution can be resampled to this beam if the mapped area is large enough.

Unfortunately, most HIFI observations were only single-point observations, not full maps, so that such a convolution is impossible. To derive scaling factors that describe the translation between the measured intensities and the intensity that would be obtained in an beam, we have to assume a source geometry of the emission. Instead of using any analytic geometry, we use the actually measured distribution of warm dust seen in the sub-mm. By assuming that the spatial distribution of all PDR tracers roughly follows the warm dust, we derive scaling factors for the line intensities at different beam widths, by convolving the sub-mm continuum map with the different beam sizes and picking ratios between the convolved intensities at the measured positions. As a continuum map at IRS1, we used the combination of the SPIRE 250 m ( beam size ) and SCUBA 450 m image ( beam size, Holland et al. 1999), because IRS1 is saturated in SPIRE 250 m, whereas the observed area of SCUBA 450 m is too small to make a convolution map with the beam size of . We regrid the SCUBA 450 m image to the same grid as SPIRE 250 m, determine the scaling factor between the SCUBA 450 m and the SPIRE 250 m maps from the overlapping area, and replace the saturated pixels of SPIRE 250 m with the scaled SCUBA data. As this combination implies some arbitrariness, we tested four different approaches. We derive the scaling factor in a least squares fit using either (1) all the valid overlapping pixels or (2) only overlapping pixels with SPIRE 250 m >100 Jy/beam. When replacing SPIRE pixels, we replace either (1) only saturated pixels, or (2) the full square area (  pixels) containing all saturated pixels. The combination of these provide 4 different beam scaling factors, which are consistent to within 3%. Taking the average of these 4 values, we derive the final factors as shown in Table A.1. A direct convolution to was possible for the ground-based maps that were observed with a smaller beam, such as the JCMT CO(3-2) map. All the resulting intensities are summarized in Table A.2.

Table A.1:   The scaling factors between the different beam size observations, which should be multiplied to the line intensity to estimate the one in a beam.

Table A.2:   List of the complementary data.

Appendix B: The clumpy PDR model

To model the far-infrared line emission from S140, we used a superposition of spherical clumps described by the KOSMA- PDR model (Röllig et al. 2006) that represent an ensemble of clumps with a fixed size-spectrum (Cubick et al. 2008). The KOSMA- PDR model simulates a spherical cloud with a radial density profile given by

The constant c determines the dynamic range that is covered by the power-law density decay. The spectrum of PDR clumps is characterized by the clump mass spectrum

where the factor a is determined by the total mass of clumps within the beam, , and the mass-size relation

which implicitly defines the surface density of the individual clumps . The factor C is determined by the average ensemble density . Guided by the clump-decomposition results from Heithausen et al. (1998), we fix the parameters of the spectrum to be , , , and c=5. The boundaries of the clump size distribution and are used as free parameters with the constraint that the maximum clump mass cannot exceed half of the mass of the total ensemble.

Every individual clump is treated as a spherically symmetric configuration illuminated by an isotropic external UV radiation field, specified in terms of the average interstellar radiation field,  erg cm^-2 s^-1 in Draine units, and cosmic rays producing an average ionization rate,  s^-1. The internal velocity dispersion of molecules within the clumps is fixed to 1 km s^-1. The model computes the stationary chemical and temperature structure by solving the coupled detailed balance of heating, line and continuum cooling, and the chemical network using the UMIST data base of reaction rates (Woodall et al. 2007) expanded by separate entries for the ¹³C chemistry (see Röllig et al. 2007, for details). The chemical network currently does not include ¹⁸O, so that C¹⁸O predictions can only be obtained by scaling the ¹³CO values ignoring fractionation between the two species. As this ignores the different self-shielding of ¹³CO and C¹⁸O, the model results for C¹⁸O are less reliable than for the other lines.

In the superposition of clumps, the line emission from the different clumps is simply added assuming that the velocity dispersion between the clumps is large enough, so that they do not shield each other in position-velocity space. This is valid for most species, except for the [O  I] emission, which is opticallyvery thick ( ), so that the lines are much broader than the velocity distribution. Therefore, the model is unable to provide any reliable estimate of the [O  I] intensities. For the continuum extinction of the UV radiation, the situation is different. There, mutual shading of the clouds is relevant, leading to the concept of different clump ensembles that ``see'' different UV fields if the average ensemble extinction exceeds an of about unity.

The parameters of the clump mass spectrum imply that most of the mass is actually contained in the largest clumps that also have the maximum column density or , respectively. The dependence of and clump size on clump mass is given by

and

In terms of the total clump surface or the total solid angle of the different clumps, we find about equal contributions from each logarithmic mass bin in the ensemble (Eq. (16) in Cubick et al. 2008). Consequently, we find a non-trivial dependence of the intensity in the different HIFI lines on the clump mass. Figures 3 and 5 from Cubick et al. (2008) show that the [C II] emission is dominated by the largest clumps, while the high-J CO lines are dominated by the smallest clumps. A complex, non-monotonic behavior is observed for the lines from atomic oxygen and mid- to low-J CO isotopes.

As the clump spectrum is purely observationally based, it has no direct relation to a stability criterion. We indeed find that both the most massive clumps are unstable to gravitational collapse and that the smallest clumps will be dispersed on the timescale of a few million years. Therefore, the spectrum can only be considered as a snapshot of interstellar turbulence that reflects the density structure over a timescale of 10⁶-10⁷ years. The assumption of a steady-state chemistry and energy-balance is therefore only applicable if all rates are higher. This holds for the dense clumps in the S140 model fit with densities above 10⁴ cm^-3, but for lower densities, an explicitly time-dependent modeling would be required (Viti et al. 2006).