Online material

Appendix A: ¹³CO and C¹⁸O spectra

A sample spectrum of ¹³CO of all the fields are shown in Fig. A.1 and A.2. The spectra are from the ¹³CO peak position of each field. The C¹⁸O spectrum is shown from the same position; the baseline has been moved to −2.0 K.

	Fig. A.1 Observed 13CO and C18O spectra at the 13CO peak position. The x-axis shows the velocity and the y-axis shows the main beam temperature. For plotting, the C18O spectra have been shifted by 2 K.
Open with DEXTER

	Fig. A.1 continued.
Open with DEXTER

Appendix B: N₂H⁺

The spectra with N₂H⁺ detections, besides the field G86.97–4.06 in Fig. 3, are shown in Fig. B.1.

Fig. B.1 N2H+ spectra observed toward G92.04+3.93, G93.21+9.55, G98.00+8.75, G105.57+10.39, and G132.12+8.95. The field G86.97–4.06 is shown in Fig. 3. The red dashed line is the fit to the hyperfine spectra and the lower subframe shows the fit residuals. The main beam temperature of the 23−12 component, the fitted radial velocity, the FWHM line width (km s-1), and the residual rms noise (as main beam temperature) are given in the frames.

Open with DEXTER

Appendix C: Radiative transfer models

	Fig. C.1 Examples of the modeled 13CO (upper frames) and C18O spectra (lower frames) for the northern (left frames) and southern (right frames) positions in the field G131.65+9.75. The histograms show the observed spectra and the continuous red lines the model predictions. The model densities were derived from continuum modeling with OH dust, assuming a narrow LOS density profile.
Open with DEXTER

In Sect. 4 the dust emission was analyzed assuming a constant temperature along the line-of-sight (LOS), but this may underestimate the true column density of externally heated, optically thick clumps (Malinen et al. 2011; Juvela et al. 2013). Similarly, the ¹³CO(1–0) and C¹⁸O(1–0) lines were analyzed using the LTE assumption, without the possibility of independent estimates of their relative abundances. To examine these questions, we carried out radiative transfer modeling where the density distribution was first derived from dust continuum observations and was then used as a basis for modeling the lines. The modeling was limited to the two positions in the field G131.65+9.75.

Appendix C.1: Modeling of dust surface brightness

We extracted 5′ × 5′ continuum surface brightness maps centered on the selected positions and resampled the data on 3″ pixels. The maps are 100×100 pixels in size and corresponding model clouds were constructed using a Cartesian grid of 100 × 100 cells. In the LOS direction the density distribution was assumed to follow a Plummer-like (Whitworth & Ward-Thompson 2001; Plummer 1911) function , with a central flat part with R_flat equal to 0.03 pc (not well resolved with the employed discretization). Corresponding to the apparent clump sizes in the plane of the sky, the FWHM of the density distribution was set to ~17 pixels, which corresponds to ~50″ or a linear scale of 0.25 pc at the distance of 1070 pc. This may overestimate the size because of the effects of beam convolution and radial temperature gradients in the clumps. For this reason, and to check the general sensitivity to the LOS extent, we also calculated another set of models with FWHM at half of the value given above. Note that the clump size can also be significantly larger along LOS than in the plane of the sky. There is even some bias in this direction because the emission from elongated clumps and filaments becomes stronger when they are aligned along LOS.

We performed the calculations iteratively, and on each iteration we solved the dust temperature distributions and calculating model predictions of the surface brightness that we then convolved to the resolution of the observations. The calculations were carried out with a Monte Carlo radiative transfer program (Juvela 2005). The initial external radiation field corresponded to that of Mathis et al. (1983). The modeling was performed with two dust models. The first, in the following MWD, represents dust in normal diffuse interstellar medium (Li & Draine 2001). The other one, in the following OH, was taken from Ossenkopf & Henning (1994) and corresponds to dust that has coagulated and accreted thin ice mantles over a period of 10⁵ yr at a density 10⁶ cm^-3. In our calculations, the dust opacities κ(250 μm) were 0.045 cm² g^-1 for MWD and 0.22 cm² g^-1 for OH, the value of Sect. 4 falling between the two. The value of κ is crucial because it affects the column density, an important parameter of the subsequent line modeling.

In the plane of the sky, the column density corresponding to each map pixel was adjusted by comparing the observed 350 μm surface brightness with the model prediction. The external radiation field was adjusted so that finally the 160 μm and 500 μm predictions also agreed with the observations to within 10%. The observations could be fitted well with both dust models, with an external radiation field 70−80% of the Mathis et al. (1983) values. Because we used background-subtracted surface brightness data, the model represents only the inner parts of the cloud without the diffuse envelope. Therefore, the radiation field in the models is somewhat weaker that the full radiation field outside the cloud. The column densities are listed in Table C.1.

The values obtained with the OH dust model are close to the column densities estimated in Sect. 4. With MWD, the column densities are higher and in the northern point by more than the ratio of dust opacities, ~5. For a given dust opacity and radiation field, there is a maximum surface brightness that can be produced with any column density. Thus, for a too small value of κ, the column density of the model might be grossly overestimated. When estimated with the NICER method (using 2MASS stars, a spatial resolution of two arcminutes, and a value of R_V = 3.1), the visual extinction of northern clump is less than 3 mag. Taking the difference in the resolution into account, this is still consistent with the Sect. 4 estimates and the result from the models with OH dust. However, the A_V measurement appears to rule out the values obtained with MWD dust (assuming the A_V is not severely underestimated either because of very clumpy column density structure or the presence of foreground stars) and give some support to the idea of dust opacity higher than that of diffuse medium.

Appendix C.2: Modeling of the ¹³CO(1–0) and C¹⁸O(1–0) lines

We modeled the ¹³CO(1–0) and C¹⁸O(1–0) lines separately, taking the density distribution directly from the continuum models. We only modeled the spectra toward the center of the clumps. The fractional abundance and kinetic temperature were assumed to be constant but in the non-LTE models the excitation temperature does vary and gives more weight to the dense regions. The velocity field was initialized by giving each cell a random velocity vector with σ_3D = 1.0 km s^-1 and assuming a turbulent line width with Doppler velocity km s^-1. Thus the initial “microturbulence” within the cells is slightly larger than the “macroturbulence” between the cells. In the actual calculations, to match the observed line widths, both velocity components are scaled by the same number, typically by ~0.3−0.4, and the thermal line broadening is added to the turbulent line widths. The predictions of the models are optimized regarding the line width (the scaling mentioned above) and the line intensity that is adjusted by changing the molecular abundance. There are four cases for each position corresponding to two different assumptions of the LOS cloud extent and the two different dust models. Furthermore, some models were also calculated with a kinetic temperature of T_kin = 12.0 K, instead of the default assumption of T_kin = 10.0 K. Again, the true kinetic temperature is unknown, but the comparison between T_kin = 10.0 K and T_kin = 12.0 K gives some idea of the associated uncertainties.

We performed the line calculations with the Monte Carlo program described in Juvela (1997). The obtained abundances

are listed in Table C.1. Concentrating on the models based on continuum modeling with OH dust, the ¹³CO values are on the order of the canonical value of 10^-6 and the estimates are similar for both assumed values of T_kin. However, because the abundances directly depend on the assumed column density, and thus the values of dust κ, the absolute values are very uncertain. The relative abundance between ¹³CO and C¹⁸O should be more reliable, as suggested by the similarity between the OH and MWD cases and the two cases of LOS density distribution. The abundance ratio is ~10 and thus larger than the value of 5.5 that was assumed in Sect. 3.

© ESO, 2015