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Appendix A: Observations

Fig. A.1 Observations of CB4. Digitized Sky Survey (DSS) red, Herschel SPIRE 250 μm, 12CO (J = 2−1), 13CO (J = 2−1), C18O (J = 2−1), and N2H+ (J = 1−0). The gray circles in the lower right corners indicate the respective beam sizes. The square marker indicates the center of the starless core. The dashed contour marks NH = 1021 cm-2. The white circles indicate the regions of which 1D-profiles were obtained by azimuthally averaging.

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Fig. A.2 Observations of CB17. DSS red, Herschel SPIRE 250 μm, 12CO (J = 2−1), 13CO (J = 2−1), C18O (J = 2−1), and N2H+ (J = 1−0). The gray circles in the lower right corners indicate the respective beam sizes. The square marker indicates the center of the starless core, the asterisk the position of the Class I YSO. The dashed contour marks NH = 1021 cm-2, the solid contour NH = 1022 cm-2. The white circles indicate the regions where 1D-profiles were obtained by azimuthally averaging.

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Fig. A.3 Observations of CB26. DSS red, Herschel SPIRE 250 μm, 12CO (J = 2−1), 13CO (J = 2−1), C18O (J = 2−1), and N2H+ (J = 1−0). The gray circles in the lower right corners indicate the respective beam sizes. The square marker indicates the center of the starless core, the asterisk the position of the Class I YSO. The dashed contour marks NH = 1021 cm-2, the solid contour NH = 1022 cm-2. The white circles indicate the regions where 1D-profiles were obtained by azimuthally averaging.

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Fig. A.4 Observations of CB27. DSS red, Herschel SPIRE 250 μm, 12CO (J = 2−1), 13CO (J = 2−1), C18O (J = 2−1), and N2H+ (J = 1−0). The gray circles in the lower right corners indicate the respective beam sizes. The square marker indicates the center of the starless core. The dashed contour marks NH = 1021 cm-2, the solid contour NH = 1022 cm-2. The white circles indicate the regions where 1D-profiles were obtained by azimuthally averaging.

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Fig. A.5 Observations of B68. DSS red, Herschel SPIRE 250 μm, 12CO (J = 2−1), 13CO (J = 2−1), C18O (J = 2−1), and N2H+ (J = 1−0). The gray circles in the lower right corners indicate the respective beam sizes. The square marker indicates the center of the starless core. The dashed contour marks NH = 1021 cm-2, the solid contour NH = 1022 cm-2. The white circles indicate the regions where 1D-profiles were obtained by azimuthally averaging.

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Fig. A.6 Observations of CB130: DSS red, Herschel SPIRE 250 μm, 12CO (J = 2−1), 13CO (J = 2−1), C18O (J = 2−1), and N2H+ (J = 1−0). The gray circles in the lower right corners indicate the respective beam sizes. The square marker indicates the center of the starless core, the asterisk the position of the Class I YSO. The dashed contour marks NH = 1021 cm-2, the solid contour NH = 1022 cm-2. The white circles indicate the regions where 1D-profiles were obtained by azimuthally averaging.

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Fig. A.7 Observations of CB244: DSS red, Herschel SPIRE 250 μm, 12CO (J = 2−1), 13CO (J = 2−1), C18O (J = 2−1), and N2H+ (J = 1−0). The gray circles in the lower right corners indicate the respective beam sizes. The square marker indicates the center of the starless core, the asterisk the center of the Class 0 protostellar core. The dashed contour marks NH = 1021 cm-2, the solid contour NH = 1022 cm-2. The white circles indicate the regions where 1D-profiles were obtained by azimuthally averaging.

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Appendix B: Hydrogen density and dust temperature maps

	Fig. B.1 Dust temperature map of CB4 overlaid with contours of the hydrogen density. They mark densities of 102, 103, and 104 cm-3. The square indicates the center of the starless core.
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	Fig. B.2 Dust temperature map of CB17 overlaid with contours of the hydrogen density. They mark densities of 102, 103, 104, and 105 cm-3. The square indicates the center of the starless core.
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	Fig. B.3 Dust temperature map of CB26 overlaid with contours of the hydrogen density. They mark densities of 103, and 104 cm-3. The square indicates the center of the starless core.
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	Fig. B.4 Dust temperature map of CB27 overlaid with contours of the hydrogen density. They mark densities of 103, 104, and 105 cm-3. The square indicates the center of the starless core.
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	Fig. B.5 Dust temperature map of B68 overlaid with contours of the hydrogen density. They mark densities of 103, 104, and 105 cm-3. The square indicates the center of the starless core.
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	Fig. B.6 Dust temperature map of CB130 overlaid with contours of the hydrogen density. They mark densities of 103, 104, and 105 cm-3. The square indicates the center of the starless core.
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	Fig. B.7 Dust temperature map of CB244 overlaid with contours of the hydrogen density. They mark densities of 103, 104, and 105 cm-3. The square indicates the center of the starless core.
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Appendix C: LTE Analysis

Appendix C.1: Model

We estimated the molecular column densities of ¹³CO, C¹⁸O, and N₂H⁺ in a first step with a simple and well-established approach. For completeness, we briefy describe here this simplified approach and the results and discuss the differences and drawbacks with respect to the full chemical modeling.

We do not model the emission of the ¹²CO (J = 2−1) transition, since it becomes optically thick already at n_H < 10⁴ and therefore does not trace the regions of expected freezeout. At these low densities, gas and dust temperatures might also be decoupled (Galli et al. 2002), which is an additional obstacle for interpreting the ¹²CO emission.

The method is described in Stahler & Palla (2005). It assumes LTE and a constant gas temperature along the LoS. Since we do not have an independent measurement of the gas temperature, we make the simplifying assumption that the kinetic gas temperature is the same as the dust temperature we obtained from the LoS-averaged black-body-fitting of the continuum data in Launhardt et al. (2013). This is justified in the dense interiors of the starless cores, but may no longer be strictly valid in the outer parts at hydrogen densities below a few 10⁴ cm^-3.

To prepare the analysis, we obtain maps of the flux in the observed lines by integrating over the velocity axis of the spectral cubes. Maps of the linewidths of the CO isotopologues were derived from Gaussian fits to the spectra. For N₂H⁺ we use the hfs-fitting routine provided with the CLASS package of GILDAS⁹. This routine allows fitting the full hyperfine structure of the J = 1−0 transition and thus also derives the optical depth of the lines. The frequency offsets and relative strengths of the individual lines are adopted from Caselli et al. (1995). With these intermediate results at hand we can derive the molecular column densities using (C.1)where ν₀ is the frequency of the transition, Δν the observed linewidth, Q the partition function of the rotational levels, Δτ the total optical thickness of the line, A_ul the Einstein parameter of the transition, g_i the relative statistical weights of the upper and lower levels, T₀ = hν₀/k_B, and T_ex the excitation temperature of the molecules. Since we assume LTE, we set T_ex = T_gas = T_{dust,   MBB}. The partition function Q is given by (C.2)where B = 55   101.011 MHz is the rotational constant for ¹³CO, B = 54   891.420 MHz for C¹⁸O, and B = 46   586.867 MHz for N₂H⁺ (Pickett et al. 1998). While the optical depth of N₂H⁺ could be determined directly by comparing the strength of the individual hyperfine components, we need to apply the “detection equation” in order to derive the optical depth of the CO lines: (C.3)\newpagewhere f(T) ≡ (exp(T₀/T)−1)^-1, T_bg = 2.73 K, and T_B taken as the peak value of the Gaussian fits.

One-dimensional profiles of the resulting maps were obtained by azimuthally averaging around the core centers. In case of asymmetries, a segment of the circle in this direction has been masked for the averaging task. The regions that have been taken into account for deriving the 1D-profiles are indicated in Figs. A.1–A.7.

Appendix C.2: Results

The derived radial profiles of the molecular column densities of ¹³CO, C¹⁸O ,and N₂H⁺ are presented in Fig. C.1. We find signs of depletion of ¹³CO in all cores except for CB 4, which is the most tenuous core of the studied sample. The ¹³CO column density of the other cores decreases constantly with the increasing hydrogen column density. The results for ¹³CO are, however, affected by optical depth effects, as well as deviations of the gas temperature from the LoS-averaged dust temperature and sub-thermal rotational excitation.

The derivation of C¹⁸O column densities is less influenced by these effects since it is a rarer isotopologue (a factor of ~7 lower abundance as compared to ¹³CO) and since its emission comes from more restricted regions with higher gas densities. The plots of the ¹³CO column densities vs. visual extinction (top left panel of Fig. C.1) yield a remarkable difference to those of the C¹⁸O column densities. The relative abundance of ¹³CO drops continuously with increasing extinction, indicating central depletion of this species. While this behavior is also found for C¹⁸O, its relative abundance also drops toward low hydrogen column densities and peaks between an A_v of 5 to 10 mag. The drop toward lower extinction can be explained by a weaker self-shielding of this rare isotopologue, which in turn leads to photodissociation of C¹⁸O in the envelopes where ¹³CO is already well shielded. The chemical modeling, however, suggests that the UV radiation is already attenuated by several magnitudes in these regions compared to the nominal strength of the ISRF (see Sect. 4.4.5). The difference in the profiles of both species becomes more obvious from the ratio of both column densities. The ratio N(¹³CO)/N(C¹⁸O) decreases continuously with increasing hydrogen column density in all starless cores. Interestingly, it even drops below the usually assumed ratio of 7 for the ISM. The change in the N(¹³CO)/N(C¹⁸O) ratio could thus not only be due to different self-shielding of both species but also partly due to reactions that increase the abundance of C¹⁸O with respect to ¹³CO due to ion-molecule exchange reactions in cold and dense environments (e.g., Langer et al. 1984).

Where the N₂H⁺ emission is strong enough to fit the hyperfine structure, we also derive column densities for this molecule. We find that the ratio N(N₂H⁺)/N_H is roughly constant within the globules (see bottom row of Fig. C.1). This finding contrasts with the results of our advanced approach using chemical modeling and a subsequent line-radiative transfer. There we find depletion of N₂H⁺ in the centers of the majority of the globules (see Sect. 4.4.3 and Fig. 6). This demonstrates the limitation of the often-used LOS-averaged analysis.

Fig. C.1 Results from the LTE-analysis. Plotted are a) the relative column densities of 13CO against radius b) and against the hydrogen column density, c) the relative column densities of C18O against radius d) and against the hydrogen column density, e) the ratios of N(13CO)/N(C18O) are plotted against radius f) and against the hydrogen column density, g) the relative column densities of N2H+against radius, h) and against the hydrogen column density. The column densities of N2H+ in CB 4 and CB 26 could not be derived, since the emission in these globules is too weak and so are missing in the plots.

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© ESO, 2013