Astron. Astrophys. 363, 755-766 (2000)

5. Discussion

5.1. Comparison of various bands

We calculated the ratio between the dust mass and the mass of the gas in the Kh 15 core (see Sects. 4.2 and 4.3) and obtained 1:50 and 1:120 using the 15 K and the 17 K dust temperatures, respectively. Derivation of the mass of the gas using ¹³CO relative abundances valid for star forming regions (e.g. Dickman 1978a and Duvert et al. 1986) yields an unrealistic gas-to-cold dust mass ratio of 20:1 or 50:1 when a dust temperature of 15 K or 17 K is assumed. It is unlikely that the cold dust temperature in Kh 15 is as high as 19 K which would be needed for a gas-to-dust mass ratio of 100:1. A dust temperature of 17 K, applied to calculate the dust mass, is an upper limit for the cold dust component in the Galaxy (see Lagache et al. 1998) and lower dust temperature values increase the dust mass.

Several papers investigated the relationship between the FIR intensities, the column density of CO isotopic lines and the visual extinction (see e.g. Laureijs et al. 1989, 1991, 1995). The ratio of the 100 µm intensity and the visual extinction varies from cloud to cloud between 2 and 10 MJysr^-1mag^-1 and usually a denser cloud shows a lower value of this ratio. The ratio of the 100 µm excess and the ¹³CO (J=1-0) integrated intensity is in the range of 1.4 - 5.3 . We discuss these relationships for Kh 15 below.

To probe a larger area around Kh 15, we have constructed a scatter plot of the 100 µm emission , derived from a galactic background removed ISSA plate for different subfields (see Table 1), and visual extinction , derived from Wolf diagrams with the help of the method described in Sect. 4.1 (see Table 4). Removal of the galactic background emission was done following Boulanger & Pérault (1988). The slope of the linear least square fit is . Using (Dickman 1978b), the resulting slope for blue extinction 5.1 MJysr^-1mag^-1 is closed to 5.9 obtained for LDN 1780 (Laureijs et al. 1995).

We have also investigated these correlations using our DSS star counts (See Sect. 3.1.2). Comparing the COBE calibrated HIRES 100 µm intensities averaged over the 33´ sized reseau of the star count data, we have found the following relation for Kh 15:

(see also Fig. 8). The correlation coefficient is 0.72. The value of the slope is in a good agreement with the values found by Laureijs et al. (1995) towards the L134 cloud complex (2.1, 2.9 and 3.7 for LDN 183, LDN 134 and LDN 169, respectively; see their Table 2). The two distinct values of the slopes (5.1 and 2.5 from Wolf-diagrams and DSS star counts, respectively) are not in contradiction if we note that they probe regions of different densities and probably different dust compositions. In the outer regions of Kh 15 the 60 µm and 100 µm radiation is well correlated (indicating cirrus-like emission) and accordingly shows little variations, therefore the - A comparison is not presented here.

Fig. 8. Correlation between and . See the text below for the derived regression parameters.

Assuming that integrated intensities of CO isotopic lines are proportional to or , we have derived regression parameters from least-squares fits, presented in Fig. 9 and Table 6. To compare the Nagoya ¹³CO (J=1-0) data and the 60 and 100 µm HIRES images, the latter have been convolved to Nagoya-4m resolution (). As one can see from Table 6 and Fig. 9 a and b, is well correlated with both or . The resulting parameters are close to the values found in other dark clouds e.g. by Laureijs et al. (1995).

Fig. 9. Correlation between CO (J=1-0)) (Nagoya-4m) and (a ) and (b ).

Table 6. Results of the FIR emission - ¹³CO (J=1-0) integrated intensity correlation analysis. The columns are: (1) the name of correlated quantities; (2) the slope of the linear fit; (3) the constant of the linear fit; (4) level of correlation

5.2. Stability of Kh 15:

The dynamical state of the Kh 15 core was investigated following Liljeström (1991). If the gas motions in the ¹³CO core are determined by gravitation only the relation between the three-dimensional velocity dispersion of the mean gas particle , the mass of the ¹³CO core M and the effective radius of the ¹³CO core is: , where the constant C depends on the cloud geometry and density structure. The derived three dimensional virialized velocity dispersion of the mean gas particle in the ¹³CO core area is for a homogeneous sphere and for a centrally condensed () sphere. The typical observed ¹³CO line width in the Kh 15 core is . After correcting for the line broadening due to line opacity the ¹³CO line width is . Thus the three-dimensional velocity dispersion of the gas derived from observation is (see also Liljeström 1991). The ratio is 1.5 and 1.1 for a homogeneous and a centrally condensed sphere, respectively. These values are closed enough to 1 to justify that the cloud is probably in gravitational virial equilibrium, although the external pressure was neglected in this calculation.

The analysis can be repeated following Spitzer (1978, Eq. [11-24]), taking into account the external pressure as well. In this case we assumed spherical symmetry, uniform external pressure and no magnetic field or rotation. We defined a "dynamical" temperature of the core as the Doppler temperature corresponding to the line width of the emission at the peak intensity (see e.g. Nozawa et al. 1991, Eq. [10]): , where is the mean molecular mass, is the full linewidth at half-maximum and is the Boltzmann constant. This yielded . The external pressure and its maximum value have been estimated in the same manner as described by Nozawa et al. (1991, Sect. 4.2, Eq. [10-13]). We derived and for Kh 15. We conclude that the cloud is in stable equilibrium, since and .

5.3. Connection of Kh 15 to its neighbourhood

We have shown in Sect. 4.1, that Kh 15 and the NW-part of GIRL126+10 are at similar distances ( and respectively) within the uncertainities and taking into account the 25 pc size of the loop. These distance of the loop is in an excellent agreement with the distance of LDN 1333.

Additional pointed ¹²CO (J=1-0) line measurements around the loop show similar velocities at several positions (Tóth 1997, priv. com.). The CO velocities of the dark clouds Kh 19 (Khavtassi 1955) and LDN 1333 (see Fig. 10) are 3.2 kms^-1 and 3.0 kms^-1, respectively. This implies that the distance of Kh 19 is similar to LDN 1333 i.e. 200 pc. The existence of the loop GIRL126+10 is also confirmed by the principal component analysis (see e.g. Tóth et al. 1992) of HI velocity channel maps (from Hartmann & Burton 1997). This analysis shows the loop to be the most significant structure in the velocity interval 1 kms^-1 (HI) 5 kms^-1, and this 21 cm radiation is well correlated with the 100 µm FIR emission (Kiss et al. 2000, in prep.). Furthermore Kh 15 is elongated in the direction pointing into the center of the loop GIRL126+10, indicating an interaction between the cloud and the shell in the past.

Fig. 10. HI 21 cm integrated intensity map of the FIR loop GIRL126+10 (1 5 ). Contours are from 130 with 20 steps.

We conclude from the collected multiwavelength data that Kh 15 is part of the loop structure seen at l=126^o, b=10^o, identified by us and called GIRL126+10.

5.4. The wall of the Local Bubble?

Table 4 shows the presence of a nearby extinction layer (at pc) appearing in most of the subfields of the Schmidt-plate. Sfeir et al. (1999) estimated the distance to the wall of the Local Bubble (LB) based on measurements of the equivalent widths of the NaI D line doublet, and distances measured by Hipparcos. They have found that the wall of the LB is located at 130 pc at this galactic longitude, at . This is in agreement with our estimation, thus we may consider this layer as the wall of the LB.

© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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