4 Discussion

4.1 Distance of ISOSS J20246+6540

The distance of ISOSS 20246+6540 can be estimated, relating it to its neighbours. Its nearest neighbours are L1122 (Lynds 1962), and the YDM97 CO1 (Yonekura 1997). The ¹³CO survey of Cepheus by Yonekura (1997) covers the position of ISOSS J20246+6540 and their Fig. 6a indicates a few small clouds around ISOSS J20246+6540 (i.e. YDM97 CO1, YDM97 CO2, YDM97 CO3) and one even smaller unnumbered peak very close to ISOSS J20246+6540 at $l=100\hbox{$.\!\!^\circ$ }1$ $b=15\hbox{$.\!\!^\circ$ }7$. All the listed Yonekura clouds have $v_{\rm LSR}>+2.5$ km s^-1, and they are counted into the "close group'' of clouds, which on the other hand is associated with extended FIR features around ISOSS J20246+6540. The nearest molecular clouds with negative $v_{\rm LSR}$ are YDM97 CO7, CO9, CO10 at $l\approx 103$ $.\!\!^\circ$0 $b\approx 16$ $.\!\!^\circ$7. ISOSS 20246+6540 itself has $v_{\rm LSR}=-2.7$ km s^-1. It probably belongs to one of the ISM layers of the nearby Cepheus Flare GMC, and is located at about 400 pc (Kun 1998). We note that applying the size-linewidth relation of Larson (1981) the globule may be between 100 and 400 pc.

4.2 Radiative transfer models

We have modelled the NE lobe of the bipolar globule with spherically symmetric cloud models, although the NE clump shows some deviations from spherical symmetry in both ¹²CO and ¹³CO (see Figs. 2b and c). With RA = 20$^{\rm h}$24$^{\rm m}$44$^{\rm s}$ Dec = +65 $\hbox{$^\circ$ }$40 $\hbox{$^\prime$ }$04 $\hbox{$^{\prime\prime}$ }$ as the centre position, we have averaged spectra in concentric rings with radii increasing by 10 $\hbox{$^{\prime\prime}$ }$ intervals up to a radius of 90 $\hbox{$^{\prime\prime}$ }$. The effective resolution of the averaged spectra is 40 $\hbox{$^{\prime\prime}$ }$ for the J=1-0 lines and 20 $\hbox{$^{\prime\prime}$ }$ for the J=2-1 lines.

We set the cloud parameters as follows.
(1) We assume a density distribution $n \sim r^{-1.5}$ with a density ratio 20 between the centre and the cloud surface.
(2) The kinetic temperature is assumed to rise linearly from the cloud centre. This is a crude approximation of the actual temperature structure of for a small, spherically symmetric globule without internal heating sources (e.g. Leung 1985; Nelson & Langer 1999) but will suffice for the present purposes. The temperature gradient, i.e. the difference between the outermost and innermost shells $\Delta T=0$ K, 6 K or 10 K. Higher contrast than 10 K means too high a temperature for the outer cloud, in contradiction with the observed small linewidth.
(3) Extinction-dependent relative molecular abundances $X({\rm molecule})=\frac{n({\rm molecule})}{n(H)}$ were estimated according to Warin et al. (1996). The cloud is cold, exposed to UV radiation and it has a peak visual extinction between 1 and 2 mag. In these conditions isotope selective processes result in a relative overabundance of ¹³CO and relative underabundance of C¹⁸O according to Bally & Langer (1982). When applying the Warin et al. (1996) relative abundances, we introduced an intrinsic extinction at the cloud boundary since the ¹²CO lines are not vanishing at the boundary of the NE lobe. This assumption is supported by the presence of surrounding extended cirrus-like emission seen at 100 $\mu$m on the ISSA image.
(4). Distance: 100, 200, 400, 600, 800, 1000, and 2000 pc were tested.

When the density, temperature, relative abundance distributions and the distance are set to a value allowed by the above constrains, the free model parameters are the central density ($n_{\rm c}$), the intrinsic linewidth ($\Delta v$) and the angular diameter (D) of the model cloud. The radiative transfer problem is solved with Monte Carlo simulation (Juvela 1997). The computed spectra are convolved to the resolution of the observed spectra and the quality of the fit between the two is estimated with a weighted $\chi ^2$ value. The model cloud is divided into 31 shells of equal thickness and the free parameters are optimized separately for ¹²CO and ¹³CO. We then select the set of parameters which provides the best fits for both. Since the ¹²CO observations only probe the outer layers of the cloud, the ¹²CO based estimate of the column density is uncertain. Modelling based on the ¹³CO line, however, gives surprisingly similar results when the appropriate average relative abundance value X(¹³CO $)\approx 1.1\times 10^{-6}$ is selected. The models are not sensitive to 20% changes in the average molecular abundances or density, although similar changes of the kinetic temperature or size are, critical (see Fig. 3).

Figure 3: Results of the radiative transfer modelling of the northern lobe assuming distances: 100 pc (yellow), 200 pc (lilac), 400 pc (red), 1000 pc (blue). The relative $\chi ^2$ minimum regions are plotted as shaded regions in selected planes of the parameter space. Two further contours of the relative $\chi ^2$ of 1.14 & 1.29 are overlaid. (Extinction dependent relative molecular abundances were used.) a) Density versus kinetic temperature (left); b) density versus size (right).

Synthetic spectra for C¹⁸O CS and HCO⁺ were generated with the NLTE model using the best parameter sets (lowest $\chi ^2$) from the ¹²CO ¹³CO analysis. The relative abundances were varied up to 100% and the other parameters up to 30%. The C¹⁸O lines were best reproduced assuming an average relative abundance of $X(^{13}{\rm CO})/X({\rm C}^{18}{\rm O})\approx 150$, an extreme but possible underabundance by factor of 28 (Glassgold et al. 1985). The pointed measurements supported the density and temperature results shown in Fig. 3. The derived NLTE kinetic temperature is around 11 K and assuming a distance of 400 pc the peak hydrogen density and the size of the NE lobe are $n_{\rm c}=6.7\times 10^4$ cm^-3 and 0.12 pc respectively. The column density estimate is $N({\rm H}_2)\approx 2\times 10^{21}$ cm^-2. This result is in agreement with the column density derived from the FIR data. The total gas mass would be $\approx$ $3~{M}_{\odot }$.

With $N({\rm H}_2) \sim 10^{21}$ cm^-2, the visual extinction towards the cloud centre is $A_{\rm V} \approx 1$ (Bohlin et al. 1978) and the cloud is optically thick for UV photons unless it is very clumpy. External heating, however, is reduced by the surrounding ISM, which is represented by the nonvanishing ¹²CO lines. This may be the reason that a moderate 6 K temperature contrast was found to be more likely than a 10 K contrast. A similar temperature profile was found by Ciardi et al. (2000) in one of the dense cloud cores of L 1082.

Although the SW clump is clearly elongated similar modelling was carried out for that part of the cloud. Observed spectra were averaged over annuli at radii up to 50 $\hbox{$^{\prime\prime}$ }$ from the clump centre. Assuming a model where the kinetic temperature increases linearly from the centre, we obtain a peak column density of $N({\rm H}_2)=2.9\times 10^{20}$ cm^-2 based on the CO spectra.

4.3 Frequency of faint globules

In the Yonekura (1997) data ¹³CO spectra were found for one of the 5 clouds. ISOSS J20215+6820 appeared as a small ( $FWHM\le 5\hbox{$^\prime$ }$) isolated molecular cloud with $M\approx 2~M_{\odot}$ when $T _{\rm ex}=11$ K and a distance of d=400 pc was assumed (Yonekura 2002). The 2 ISOSS sources without opaque cores have their nearest cloud neighbours outside a $15\hbox{$^\prime$ }$ search radius. The 3 opaque cloudlets are separated from their companions by about $10\hbox{$^\prime$ }$ (see also Table 1).

All the 5 globule like sources were found inside the fainter half of the studied region, i.e. in $95\hbox{$^\circ$ }<l<105\hbox{$^\circ$ }$, $10\hbox{$^\circ$ }<b<20\hbox{$^\circ$ }$, where the ISOSS slew coverage was above 70%, and the average 170 $\mu$m sky brightness is $\approx$30 MJy sr^-1. This kind of sources may be similarly common in other galactic regions. However detecting them by ISOSS may be more difficult at regions with higher FIR background/foreground brightness values.