4 Results and analysis

Figures 3 and 4 present the 12, 25, 60, and $100~\mu$m background-subtracted IRAS co-added images of GF 17 and GF 20. The $12~\mu$m and $25~\mu$m images reveal few point sources toward GF 17 and GF 20. Some of these sources are confirmed young stellar objects (mostly T Tauri stars) associated with their parent cloud, while other sources are simply unrelated background and/or foreground objects. The locations of confirmed young stellar objects within each cloud are indicated by the filled star symbols. Of the eight T Tauri stars known to be associated with GF 17 (Schwartz 1977), only four are seen in our IRAS field. These are found in regions of visual extinction smaller than 1 mag (Andreazza & Vilas-Boas 1996), and distributed around the main core region of GF 17. Four of the five T Tauri stars associated with GF 20 are seen in our IRAS field. The strongest $25~\mu$m source, and almost coincident with the peak of $100~\mu$m emission, is the extremely active T Tauri star RU Lupi (Schwartz 1977). Andreazza & Vilas-Boas (1996) estimate the visual extinction to this source to be ${\sim} 3.8$ mag from optical star counts. The remaining T Tauri stars are found in regions of visual extinction smaller than 1 mag (Andreazza & Vilas-Boas 1996).

Figure 3: Background-adjusted IRAS co-added images obtained toward GF 17. Filled stars show the positions of T Tauri stars associated with GF 17. The intensity scale in each panel is 106 Jy ster-1, starting at $0.4\times 10^{6}$ Jy ster-1 (mean noise level). For clarity, contours of $100~\mu$m emission at 6, 8, 10, 12, 14, and $15\times 10^{6}$ Jy ster-1 are shown.

Figure 4: Background-adjusted IRAS co-added images obtained toward GF 20. Filled stars show the positions of T Tauri stars associated with GF 20. The white star indicates the position of the extremely active T Tauri star RU Lupi. The intensity scale in each panel is 106 Jy ster-1, starting at $0.3\times 10^{6}$ Jy ster-1 (mean noise level). For clarity, contours of $100~\mu$m emission at 8, 10, 12, 14, and $16\times 10^{6}$ Jy ster-1 are shown.

4.1 IRAS cloud morphology

The IRAS wide-field, high dynamic range images clearly reveal the filamentary nature of GF 17 and GF 20. The spatial distribution of dust emission in these globular filaments is not irregular in shape, but rather is extremely elongated. The $100~\mu$m emission from GF 17 peaks at a main core region, and defines a filamentary region toward the east. In GF 20, the $100~\mu$m emision peaks at a main core region associated with RU Lupi. A second strong peak of $100~\mu$m emission is located about $5^{\prime}$ to the south of RU Lupi. A third peak of $100~\mu$m emission appears within the filamentary part of GF 20. Like GF 17, the filamentary structure in GF 20 is well delineated at $100~\mu$m, extending to the northeast, away from RU Lupi. Table 1 summarizes the $60~\mu$m and $100~\mu$m peak fluxes of dust emission from selected regions within each cloud. The positions in Cols. 3 and 4 were derived from the $100~\mu$m images. Columns 7, 8, and 9 give average dust temperatures, optical depths, and visual extinctions observed within each region.

   

Table 1: Far-infrared properties of GF 17 and GF 20.

				Peak Brightness
				(MJy ster-1)
		RA	Dec			T60/100	$\tau _{100}$	AV
Cloud	Region	(1950)	(1950)	$60~\mu$m	$100~\mu$m	(K)	( $\times10^{-5}$)	(mag)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
GF 17	main core	$15^{\rm h}59^{\rm m}00^{\rm s}$	$-41^{\circ}50{'}$	4.8	15.4	43	0.7	0.4
	filament	16 00 30	$-41^{\circ}52{'}$	3.2	11.0	42	0.4	0.2
GF 20	main core(a)	15 53 30	$-37^{\circ}47{'}$	3.4	17.1	31	3.1	0.7
	main core(b)	15 53 40	$-37^{\circ}38{'}$	4.4	17.2	30	2.8	0.6
	filament	15 55 00	$-37^{\circ}33{'}$	2.3	12.1	33	1.6	0.4
	filament	15 56 00	$-37^{\circ}28{'}$	1.8	10.0	32	1.5	0.4

^(a) South of RU Lupi.
^(b) Associated with RU Lupi.

GF 17 and GF 20 share an interesting characteristic in their dust emission. Note that we do not see the clouds boundaries at 12 or $25~\mu$m. This is unlike the $\rho$ Ophiuchi cloud which has IR boundaries clearly delineated at both $12~\mu$m ( $hc/k\lambda\sim1000$ K) and $100~\mu$m ( $hc/k\lambda\sim100$ K), as shown by Jarrett et al. (1989). These authors concluded that the IR emission from $\rho$ Ophiuchi needs to be modeled as arising from two physically distinct populations of dust grains. Our IRAS images thus suggest that the IR emission from GF 17 and GF 20 can be modeled as arising from one single population of "cool'' dust grains, and we proceed with the assumption that the emission at 60 $\mu$m and 100 $\mu$m probably arises from large dust grains in equilibrium with the radiation field. However, we caution that part of the 60 $\mu$m emission may arise from transiently excited particles (Puget & Léger 1989).

4.2 Dust color temperature and optical depth

As mentioned above, the derived temperatures should be viewed with a great deal of caution. For the optically thin emission detected from these clouds by IRAS, the exponential nature of the flux dependence on temperature leads to a bias toward higher derived temperatures than are physically present along the line of sight. Hence, all the temperatures derived are weighted toward the warmer parts of the clouds and not the mass-averaged bulks of the clouds. Note, then, that all temperatures are upper limits, and all opacities are lower limits.

Figures 5 and 6 present images of the dust color temperature, T_60/100, and dust optical depth, $\tau _{100}$, for GF 17 and GF 20, respectively. The dust temperatures we derive are in reasonable agreement with the range of temperatures (20-40 K) derived by Jarrett et al. (1989) for the $\rho$ Oph cloud, and larger than the values (20-25 K) found by Wood et al. (1994) for the L1521 and L1506 filaments in Taurus. Color temperatures range from 25 to 45 K for GF 17 and from 30 to 45 K for GF 20. In GF 17, the filamentary region is warmer than the main core region, with clump temperatures of 40 K, and interclump temperatures of ${\sim}42$ K. For GF 20, this difference is less evident: the temperatures of the clumps within the filamentary region of GF 20 exhibit the same temperature (roughly 31-33 K) of the main core region. The interclump region within the filament is marginally warmer, at ${\sim}35$ K. Peaks of 43 to 46 K occur toward the T Tauri stars near the main core region of GF 20 (see Fig. 6), but care must be taken in interpreting these values, as a steep dust temperature gradient along the line of sight would be expected toward a bright point source within the cloud, invalidating the simple homogeneous model adopted here. These two stars are hot sources seen in the $60~\mu$m image which have produced unphysical depressions in the $100~\mu$m optical depth image. Away from the central regions of GF 17 and GF 20, the color temperature of the dust emiting at $60~\mu$m and $100~\mu$m smoothly rises to a maximum of about 45 K, at the optical edges of the clouds.

The highest gas temperatures (given by the CO antenna temperature) in GF 17 and GF 20 are 12.5 K and 14.1 K, respectively. Hence, dust temperatures appear to be high enough to heat the gas to those temperatures. However, our dust temperature images show that GF 17 and GF 20 are clearly limb-brightened. This means that the highest gas temperatures occur where the dust temperatures are the lowest, i.e. in the central, denser regions of the clouds. Consequently, the CO must be heated by a source of energy other than grain collisions in the bulk of the clouds. Together with the lack of young stellar objects embedded in GF 17 and GF 20, this seems to indicate that these clouds are heated externally.

Figure 5: T60/100 and $\tau _{100}$ images obtained toward GF 17. Filled stars show the positions of T Tauri stars associated with GF 17. The temperature scale is degrees Kelvin. Notice the limb brightening in GF 17, with T60/100 increasing from the inner regions toward the edges of the cloud: for clarity, we plot contours at 35 K (the innermost contour), 40 K, and 46 K (the outermost contour).

Figure 6: T60/100 and $\tau _{100}$ images obtained toward GF 20. Filled stars show the positions of T Tauri stars associated with GF 20. The temperature scale is degrees Kelvin. Notice the limb brightening in GF 20, with T60/100 increasing from the inner regions toward the edges of the cloud: for clarity, we plot contours at 32 K (the innermost contour), 35 K, and 38 K (the outermost contour).

The derived 100 $\mu$m optical depths typically range from $2\times10^{-6}$ to $1.8\times10^{-5}$ within GF 17 and from $3\times10^{-6}$ to $3.8\times10^{-5}$ in GF 20. These values are typically an order of magnitude smaller, and span a narrower range than the values derived by Jarrett et al. (1989) for the $\rho$ Oph cloud, and by Wood et al. (1994) for a sample of 43 clouds with $A_{V}\geq2$ mag, using the same method. The lower dynamic range exhibited by $\tau _{100}$ over GF 17 and GF 20 suggests that the grain population responsible for the 100 $\mu$m emission is likely to be unheated over much of the interior of the clouds, implying that we are probing the edges of GF 17 and GF 20 and not their cold, innermost regions.

4.3 Dust mass

To calculate the mass of dust in GF 17 and GF 20 we calculate the mass column density of dust grains at $100~\mu$m, $\sigma_{\rm d}$, as

$$% \sigma_{\rm d} = \frac{4}{3} (\frac{a\rho}{Q_{100}}) \tau_{100}~~({\rm g~cm}^{-2}),$$ (7)

where $\rho$ is the grain density, Q₁₀₀ is the emission efficiency at $100~\mu$m, and where we have assumed that a line of sight with column density $N_{\rm g}$ of grains having radius a, has an optical depth at $100~\mu$m given by (Hildebrand 1983)

$$% \tau_{\lambda} \simeq \pi <a>^{2} Q_{\lambda} N_{\rm g}.$$ (8)

Using an average value for $(a\rho/Q_{100})$ of $3.2\times (1000/\lambda_{\mu {\rm m}})$ for a mixture of graphite and silicate grains (Hildebrand 1983), we have

$$% \sigma_{\rm d} = 4.17\times 10^{-2}\tau_{100}~~({\rm g~cm}^{-2}).$$ (9)

Integrating the $\tau _{100}$ images over the area of each cloud (defined as the area of the contour level equal to $20\%$ of the peak $100~\mu$m opacity in the clouds), we obtain an estimate of the dust mass for GF 17 and GF 20. We find total dust masses of about $2.2\times10^{-3}~M_{\odot}$ and $5.0\times10^{-3}~M_{\odot}$ for GF 17 and GF 20, respectively. These values decrease to $6.1\times10^{-4}~M_{\odot}$ and $1.6\times10^{-3}~M_{\odot}$, respectively, if one considers only the regions covered by our molecular line maps. This would imply gas-to-dust ratios much higher than the typical gas-to-dust ratio of ${\sim}100$ in interstellar clouds. However, the derived gas-to-dust ratios for GF 17 and GF 20 are consistent with a true gas-to-dust ratio of ${\sim}100$, if we conclude that less than ${\sim}1\%$ of the dust is responsible for the far-infrared emission detected with IRAS. In fact, one should keep in mind that much of the dust in a typical dark cloud is largely undetected by IRAS because it is colder than ${\sim}20$ K. Owing to the essentially exponential dependence of the infrared emission from such regions, the emission from the cold, high-extinction cores of molecular clouds without massive star formation may be essentially invisible to IRAS.

4.4 Correlations between gas and dust

Figures 7 and 8 present ¹³CO integrated emission maps toward GF 17 and GF 20. The molecular gas emission is not uniformly distributed within the clouds. Instead, the emission is seen to arise in chains of condensations strung along their lengths, in a periodic fashion, giving these clouds an overall highly fragmented appearance. We find a remarkably good agreement between our $100~\mu$m optical depth images and our ¹³CO integrated emission maps. Our optical depth images of GF 17 and GF 20 reproduce the filamentary morphology seen in our ¹³CO maps. In particular, we see that the $100~\mu$m optical depth and ¹³CO emission images have identified the dense cores within each cloud with remarkable agreement, suggesting that the gas-to-dust ratio is nearly constant throughout these clouds.

Figure 7: 13CO integrated emission map toward GF 17. Top panel: contour levels start at 1 K km s-1 in steps of 0.3 K km s-1, and shaded contours start at 3.4 K km s-1. Bottom panel: contour levels start at 3.6 K km s-1 in steps of 0.3 K km s-1, shaded contours start at 6.0 K km s-1. The (0, 0) position corresponds to ${\rm RA}=16^{\rm h}01^{\rm m}48.6^{\rm s}$, ${\rm Dec}=-41^{\circ }51^{\prime }21^{\prime \prime }$ (J2000).

Figure 8: 13CO integrated emission map toward GF 20. Contour levels range from 1 K km s-1 to 7.5 K km s-1 in steps of 0.5 K km s-1. Shaded contours start at 2 K km s-1. The (0, 0) position corresponds to ${\rm RA}=15^{\rm h}58^{\rm m}00.0^{\rm s}$, ${\rm Dec}=-37^{\circ }42^{\prime }47^{\prime \prime }$ (J2000).

4.4.1 Far-infrared emission as a tracer of gas column density

Figure 9 presents a point by point comparison of the $100~\mu$m optical depth and ¹³CO integrated emission, I₁₃, smoothed to the spatial resolution of IRAS at $100~\mu$m, for GF 17 (top) and GF 20 (bottom), respectively. In both cases, filled circles refer to observations toward the filamentary region, and empty circles to observations within the main core region. In the case of GF 17, there is no trend (linear correlation coefficient $r\sim0.01$) of dust $100~\mu$m optical depth with ¹³CO integrated emission within the main core region. However, we find a strong correlation ($r\sim0.85$) for the filamentary region. A least-squares fit to the data within this later region yields

Figure 9: A point by point comparison of the derived 100 $\mu$m optical depth to the 13CO integrated intensity in GF 17 (top) and GF 20 (bottom). Filled and empty circles refer to observations toward the filamentary region and the main core region, respectively. The straight lines are least-squares fits to the data obtained toward the filamentary regions only (see text).

$$% \tau_{100} \,{=}\, (1.52\,{\pm}\,0.26){\times}10^{-6} + (1.28\,{\pm}\,0.10)\times10^{-6}~I_{13}.$$ (10)

For GF 20, a different behaviour is obtained: considering only the data points within the main core region, a strong linear dependence ($r\sim0.73$) is found between the dust $100~\mu$m optical depth and the ¹³CO integrated intensity. For the filamentary region, a least-squares fit returns

$$% \tau_{100} \,{=}\, (5.54\,{\pm}\,0.88){\times}10^{-6} + (3.17\,{\pm}\,0.46)\times10^{-6}~I_{13},$$ (11)

with a correlation coefficient of 0.59. Note that for the filamentary region of GF 20 the best-fit relation has considerable more scatter than the corresponding relation for GF 17. Although a correlation between $100~\mu$m optical depth and ¹³CO integrated intensity is found in both GF 17 and GF 20, the slopes of these relations are different, with the slope in the gas/dust relation for GF 20 being ${\sim}2.5$ times larger than that for GF 17. Also, the y-intercept in GF 20 is much larger than that for GF 17, indicating that for GF 20 there is substantial $100~\mu$m emission in directions where the integrated ¹³CO intensity is nearly zero. This may indicate that the background was improperly removed or that the ¹³CO emission is not tracing the entire column density of gas. Since the ¹³CO is expected to be destroyed at extinctions less than about A_V=0.5 mag, it is reasonable that there be dust and infrared emission where molecular emission cannot be detected. Another feature observed in the correlations shown in Fig. 9 is the significant number of positions (especially in GF 17) that lie above the fitted lines at large ¹³CO integrated emission. Though all lines of sight are optically thin at 100 $\mu$m, not all lines of sight are expected to be thin in ¹³CO emission, especially toward the denser parts of GF 17 and GF 20. Thus, the scatter of points above the line at large (>3 K kms^-1) ¹³CO integrated emission may indicate that the ¹³CO emission is saturated, leading to a underestimation of the gas column density therein.

A point by point comparison of the $100~\mu$m optical depth and C¹⁸O integrated intensity, I₁₈, smoothed to the spatial resolution of IRAS at $100~\mu$m, is shown in Fig. 10. For GF 17, the $100~\mu$m optical depth clearly increases with increasing C¹⁸O integrated intensity. Considering all data points, we find a very strong correlation between these two quantities. A least-squares fit yields

Figure 10: A point by point comparison of the derived 100 $\mu$m optical depth to the C18O integrated emission in GF 17 (top) and GF 20 (bottom). Filled and empty circles refer to observations toward the filamentary region and the main core region, respectively. The straight lines are least-squares fits to all the data points.

$$% \tau_{100} \,{=}\, (2.24\,{\pm}\,0.48){\times}10^{-6} + (1.19\,{\pm}\,0.09)\times10^{-5}~I_{18},$$ (12)

with a correlation coefficient of 0.85. For GF 20, the linear fit to all data points yields a much poorer (r=0.46) linear correlation

$$% \tau_{100} \,{=}\, (1.05\,{\pm}\,0.08){\times}10^{-5} + (1.09\,{\pm}\,0.25)\times10^{-5}~I_{18},$$ (13)

where we note that very few (only six) data points refer to the main core region of GF 20. However, the slope in GF 20 is similar to the one found for GF 17. This seems to indicate that additional C¹⁸O data within the main core region of GF 20 will improve the $\tau _{100}$ vs. I₁₈ relation. Hence, despite the larger scatter, we believe that the dust 100 $\mu$m optical depth and the gas column density in GF 20 are well correlated.

While the dust column density (essentially given by the dust 100 $\mu$m optical depth) only traces the depth of dust emission, the gas column density (given by the C¹⁸O integrated intensity) is the true value for the clouds, since the tracer molecule is optically thin. However, the fact that the dust column density is well correlated with the gas column density throughout GF 17 and GF 20 implies that the grains responsible for the 60 and 100 $\mu$m emission are well mixed with the gas and are heated by a radiation field that impinges these clouds in a relatively uniform fashion. The morphological similarities between the 100 $\mu$m optical depth images and the C¹⁸O integrated maps (Moreira & Yun 2002) of GF 17 and GF 20 support this idea. The good agreement between dust optical depth and C¹⁸O integrated emission in GF 17 and GF 20 then suggests that the infrared emission must originate from a substantial depth in the clouds. This is consistent with the globular nature of GF 17 and GF 20, where we expect the individual dense cores, connected by lower density material, to be more easily exposed to the local radiation field.

We thus conclude that far-infrared dust emission can reliably be used as a gas column density tracer in GF 17 and GF 20.

Figure 11: A point by point comparison of the derived dust temperature to the total column density of gas in GF 17 (top) and GF 20 (bottom). Notice that the higher dust temperatures are found towards lower gas column densities.

4.4.2 Dust and gas temperatures

A point by point comparison of the dust temperature and gas column density in GF 17 and GF 20 is shown in Fig. 11 revealing an anticorrelation between these two quantities. The spatial resolutions of both data sets were degraded to match the IRAS $100~\mu$m beam size. The temperature of the dust varies from 33 to 51 K in GF 17, and from 31 to 42 K in GF 20. Hence, the emitting dust in both clouds is substantially hotter than the gas. However, one must be cautious in interpreting these results, since, as noted above, the derived dust temperature is always weighted toward the warmest dust along the line of sight, and dust as cold as the gas will be overwhelmed by the warmer dust and will be unobservable. This explains the fact that the temperatures we calculate (see Table 1) even in the denser, starless main core regions, are significantly higher than ${\sim}20$ K, while the true gas temperatures (as derived by the ¹²CO radiation temperatures) are typically below 20 K. Despite these potential difficulties, we believe that the anticorrelation found between the dust temperature and gas column density implies that the dust is warmest where the column densities are smallest. In fact, from the dust temperature maps of GF 17 and GF 20, it is clear that the hotter dust is located at the edges of the clouds. Thus, we find further evidence for GF 17 and GF 20 being externally heated.

   
4.5 Evidence for smooth cloud edges

Our calculated dust optical depths toward GF 17 and GF 20 are small, with typical values of $\tau _{100}$ about a factor of 10 smaller than the corresponding values derived by Wood et al. (1994) for 43 nearby molecular clouds. Consequently, small (<1 mag) values of visual extinction (see Table 1) are obtained for GF 17 and GF 20 by means of Eq. (3), and we remind the reader that all extinctions quoted here are lower limits. In order to estimate the pixel-to-pixel (random) errors in A_V in each cloud, we examined about 800 pixels within a circular area which appears to have a constant extinction, and obtained a standard deviation in the extinction value of this region of 0.02 mag for both clouds. We use these values as an estimate of the pixel-to-pixel errors in A_V, but we remind the reader that this error does not include any errors caused by assuming a constant $\beta$.

Lada et al. (1994) showed that the relation between $\sigma _{\rm disp}$, the dispersion of extinction measurements within a square map pixel, and A_V, the mean extinction derived for the map pixel, can be used to characterize cloud structure on scales smaller than the resolution of the map (i.e. the size of the map pixels). In the molecular cloud IC 5146, Lada et al. (1994) and Lada et al. (1999) found that both $\sigma _{\rm disp}$ and the dispersion in the $\sigma _{\rm disp}$-A_V relation increased in a systematic fashion with increasing A_V. A similar behaviour for the L977 dark cloud was found by Alves et al. (1998). In order to investigate a $\sigma _{\rm disp}$-A_V relation for GF 17 and GF 20, we used the A_V images generated through Eq. (3). In each A_V image, we considered square map pixels (each containing about 400 image pixels) with size similar to the IRAS beam size ( $300^{\prime\prime}$) at 100 $\mu$m. A mean extinction and a dispersion within each map pixel were derived. The top panels of Figs. 12 and 13 present the $\sigma _{\rm disp}$-A_V relation for the two clouds, at $300^{\prime\prime}$ spatial resolution. The same trend observed in IC 5146 and L977 is found for GF 17 and GF 20. Both $\sigma _{\rm disp}$ and the scatter in the $\sigma _{\rm disp}$-A_V relation increase systematically with A_V in GF 17 and GF 20. A least-squares fit over the entire data sets returns the slope of the $\sigma _{\rm disp}$-A_V relation given by

$$% {\rm GF~17:}~~~\sigma_{\rm disp}/A_{V}=0.18\pm0.01~~~ \\$$ (14)

$${\rm GF~20:}~~~\sigma_{\rm disp}/A_{V}=0.34\pm0.02.$$ (15)

These values are similar to $\sigma_{\rm disp}/A_{V}=(0.21\pm0.02)$ and $\sigma_{\rm disp}/A_{V}=(0.40\pm0.01)$ found for IC5146 and L977, respectively, by Alves et al. (1998) and Lada et al. (1999), using near-infrared extinction maps at $90^{\prime\prime}$ spatial filtering. Since the estimated distance to both L977 and IC5146 is ${\sim}500$ pc, their study has a spatial resolution of 0.2 pc. Interestingly, the present IRAS study of GF 17 and GF 20 (at 150 pc) has the same spatial resolution of 0.2 pc. Hence, we are probing structures with similar physical sizes. Also interesting is the fact that from figure 9 of Lada et al. (1999) we note that for extinctions below a few magnitudes (say less than 5 mag) their $\sigma _{\rm disp}$-A_V relation is pure noise, while in our study we are sensitive to structure in the same relation but below A_V=1. Thus, the NIR- and IRAS-based techniques seem to be complementary regarding the $\sigma _{\rm disp}$-A_V relation.

Figure 12: Top panel: the relation between $\sigma _{\rm disp}$, the dispersion in the extinction measurements, and AV, the mean extinction derived within a 300'' square map pixel for GF 17. Also plotted is the least-squares linear fit to the data over the entire range of extinctions observed in the cloud. The correlation coefficient is 0.78. Bottom panel: the same relation but with a spatial filter with angular resolution of $150^{\prime \prime }$. The solid line represents a least-squares linear fit to the data over the entire range of extinctions observed in the cloud. The correlation coefficient is 0.73. Note the decrease in the slope of the $\sigma$-AV relation with increasing resolution.

Figure 13: Top panel: the relation between $\sigma _{\rm disp}$, the dispersion in the extinction measurements, and AV, the mean extinction derived within a 300'' square map pixel for GF 20. Also plotted is the least-squares linear fit to the data over the entire range of extinctions observed in the cloud. The correlation coefficient is 0.87. Bottom panel: the same relation but with a spatial filter with angular resolution of $150^{\prime \prime }$. The solid line represents a least-squares linear fit to the data over the entire range of extinctions observed in the cloud. The correlation coefficient is 0.77. Note the decrease in the slope of the $\sigma$-AV relation with increasing resolution.

Lada et al. (1994) have shown that such a relation between $\sigma _{\rm disp}$ and A_V indicate that significant structure must be present down to scales smaller than the resolution of the extinction maps. Thus, the $\sigma _{\rm disp}$-A_V relations for GF 17 and GF 20 seem to imply the presence of small-scale structure in the exctinctions toward these clouds. Recently, Lada et al. (1999) used Monte Carlo simulations to show that the form and slope of the $\sigma _{\rm disp}$-A_V relation, and hence most (if not all) of the small-scale variations in the extinction, are due to unresolved gradients in the dust distribution within IC 5146 and L977. That is to say that smoothly varying density gradients can produce the "fluctuations'' observed in extinction studies of filamentary clouds. Although (1997) found that the form of the observed $\sigma _{\rm disp}$ versus A_V relation in IC5146 is consistent with cloud structure models characterized by supersonic random motions, Lada et al. (1999) note that random spatial fluctuations in the dust distribution could exist (Thoraval et al. 1997), but at a very low level ( $\sigma_{\rm random}/A_{V}\ll 25\%$ at $A_{V}\sim30$ mag), in addition to the smooth gradients.

Consider Figs. 12 and 13 (bottom panels), where we plot the $\sigma _{\rm disp}$-A_V relation for both GF 17 and GF 20, but using a spatial filter with angular resolution of $150^{\prime \prime }$, i.e. half the IRAS beamsize at $100~\mu$m. These diagrams show that when the data are sampled with increased spatial resolution, we obtain a decrease in the slope of the $\sigma _{\rm disp}$-A_V relation. Also, note that the trend of $\sigma _{\rm disp}$ increasing with A_v appears to be independent of angular resolution. This suggests that structural variations in GF 17 and GF 20 are being increasingly resolved out with higher angular resolution. An identical behaviour was found in IC 5146 by Lada et al. (1999), who argue that such behaviour can be accounted for by a smooth, radially decreasing density gradient of the form $\rho(r)\propto~r^{-2}$, from 0 to ${\sim}20$ mag of visual extinction. In this context, since we are biased toward low (A_v<1 mag) extinctions, we conclude that the edges of GF 17 and GF 20 are likely to be characterized by a similar smooth density gradient. An investigation is underway on the modelling of the internal structures of GF 17 and GF 20 as self-gravitating cylindrical polytropes, and we defer such discussion to a future paper.

4.6 Comparison with infrared cirrus clouds and molecular dark clouds

One of the new phenomena discovered by the IRAS mission is the extensive diffuse infrared emission, strongest at $100~\mu$m, which has become known as the infrared cirrus. These highly structured extended sources are seen predominantly, but not exclusively, at 60 and 100 $\mu$m and may originate either in the interplanetary medium, the outer solar system, or the interstellar medium. The infrared cirrus have typical visual extinctions of ${\sim}0.2$ mag or less and $100~\mu$m opacities in the range $3{-}6\times10^{-5}$ (Low et al. 1984). Several studies (Blitz et al. 1984; Weiland et al. 1986; de Vries et al. 1987) have shown that molecular clouds have been found to be associated with infrared cirrus. Thus, it is of interest to compare the far-infrared emission from GF 17 and GF 20 with the more diffuse infrared cirrus clouds. The most useful means of comparison of these clouds is through the ratio of the 100 $\mu$m intensity, I₁₀₀, versus the column density of hydrogen atoms, $N_{\rm H}$. In the cirrus clouds, Low et al. (1984) derived values of $I_{100}/N_{\rm H}$ in the range 0.9-2.8 MJy sr $^{-1}/(10^{20}~{\rm H~cm}^{-2})$. Other values of $I_{100}/N_{\rm H}$ of 0.4 to 1.4 MJy sr $^{-1}/(10^{20}~{\rm H~cm}^{-2})$ were derived by Boulanger et al. (1985), Terebey & Fich (1986), and Boulanger & Perault (1988). Values of $I_{100}/N_{\rm H}$ as high as 1.9 MJy sr $^{-1}/(10^{20}~{\rm H~cm}^{-2})$ have been found for a number of molecular clouds (Boulanger 1989).

Plots of the 100 $\mu$m intensity versus molecular hydrogen column density in the edges (i.e., at those locations where the visual extinction is less than say ${\sim}2$ mag) of GF 17 and GF 20 are shown in Fig. 14. The spatial resolutions of both data sets were smoothed to the IRAS beam size at $100~\mu$m. We note that the 100 $\mu$m intensity follows closely (correlation coefficient of $r\sim0.78$) the gas column density in the vicinity of GF 17, whereas a rather poor linear trend ($r\sim0.31$) is seen for GF 20. From the least-squares fits of I₁₀₀ versus $N_{\rm gas}$ shown in Fig. 14, we have computed the ratio of $100~\mu$m intensity to total molecular hydrogen column density, and we obtain 1.78 and 0.76 MJy sr^-1 per  $10^{21}~{\rm ~cm}^{-2}$ at the edges of GF 17 and GF 20, respectively. Following Snell et al. (1989), we express these ratios in terms of hydrogen atoms to find values of 0.09 and 0.04 MJy sr^-1 per  $10^{20}~{\rm H~atoms~cm}^{-2}$ for GF 17 and GF 20, respectively. These values are in excellent agreement with the results for B18 (0.07 MJy sr $^{-1}/[10^{20}~{\rm H~cm}^{-2}]$), and significantly smaller than those found for the cirrus clouds. Hence, our clouds have lower emission per hydrogen atom than the cirrus clouds.

Figure 14: A point by point comparison of the 100 $\mu$m intensity to the total molecular hydrogen column density at the edges (AV<2 mag) of GF 17 and GF 20. Both data sets were smoothed to the spatial resolution of IRAS at 100 $\mu$m. The solid lines represent least-squares linear fits to the data.

One can also compare the ratio of 60 to $100~\mu$m intensity in our clouds with that found for the cirrus clouds. Low et al. (1984) and Terebey & Fich (1986) obtained an average I₆₀/I₁₀₀ ratio of 0.20 for the cirrus clouds. In GF 17 and GF 20, we find a systematic decrease of the I₆₀/I₁₀₀ ratio from the edges ( $I_{60}/I_{100}\sim0.3$) to the center of the clouds ( $I_{60}/I_{100}\sim0.16$). Thus, it seems that GF 17 and GF 20 have similar I₆₀/I₁₀₀ average ratios, and comparable to the corresponding ratio found in cirrus clouds. This is somewhat unexpected because due to their low visual extinctions ($A_{V}\sim$ 0.07-0.18 mag, Low et al. 1984, the dust in cirrus clouds can be heated to temperatures significantly larger than the typical IRAS dust temperatures (20-25 K) observed in the inner regions of cold dark clouds (Wood et al. 1994). Therefore, the I₆₀/I₁₀₀ ratio appears to be somewhat enhanced in GF 17 and GF 20. However, while the $100~\mu$m emission comes from large dust grains in equilibrium with the radiation field, part of the $60~\mu$m emission may arise from transiently excited particles (Puget & Léger 1989). Hence, we can interpret our enhanced I₆₀/I₁₀₀ ratios in GF 17 and GF 20 as the result of an excitation effect where small grains absorb mainly in the UV and consequently are heated only in a shell at the surfaces of GF 17 and GF 20. This is consistent with the fact that our clouds have (1) comparable peak brightness at either 60 or $100~\mu$m, (2) similar 60-100 $\mu$m colors, as given by the I₆₀/I₁₀₀ ratios, and (3) similar color morphology, in the sense that they exhibit systematic color variations correlated with the opacity (a decrease by a factor of 2 to 3 from the edges to the center).

Though the IRAS 60 and 100 $\mu$m bands do not detect the emission from most of the dust in these clouds, these bands do include most of the far-infrared luminosity. We can estimate the total far-infrared luminosities of GF 17 and GF 20 from the $60~\mu$m and $100~\mu$m images using

$$% L_{\rm FIR} = 4\pi~{d}^{2}\int{F_{\nu}{\rm d}\nu} = 4\pi~d^{2}\sum{F_{\nu}\nu}$$ (16)

where d is the distance to the clouds (taken to be 150 pc). We obtain total luminosities of ${\sim}22~L_{\odot}$ and ${\sim}30~L_{\odot}$ for GF 17 and GF 20, respectively. Considering only the regions covered by our molecular line maps, the total luminosities decrease to ${\sim}4.5~L_{\odot}$ and ${\sim}6.6~L_{\odot}$ for GF 17 and GF 20, respectively. Using the cloud masses derived above, we derive ratios of far-infrared luminosity-to-cloud mass of $0.13~L_{\odot}/M_{\odot}$ and $0.21~L_{\odot}/M_{\odot}$. For comparison, Snell et al. (1989) obtain luminosity-to-mass ratios of ${\sim}0.3~L_{\odot}/M_{\odot}$ for B18 and Heiles Cloud 2 in Taurus, Jarrett et al. (1989) derive ${\sim}0.6~L_{\odot}/M_{\odot}$ for the $\rho$ Oph dark cloud, and Clemens et al. (1991) find an average of ${\sim}0.5~L_{\odot}/M_{\odot}$ for their sample of Bok globules. Note that the luminosity-to-cloud mass ratio is a quantity which is independent of distance. The average value for the inner Galactic disk (excluding the galactic center) is $2.8~L_{\odot}/M_{\odot}$ (Scoville & Good 1987). Thus, GF 17 and GF 20 have smaller luminosity-to-mass ratios than the average Bok globule or the $\rho$ Oph dark cloud, but comparable to the luminosity-to-mass ratios found in Taurus.

4.7 Velocity structure of the clouds

The kinematics of a molecular cloud reflects the motions which brought the gas to its current configuration, and can be used to characterize the cloud's evolution. Kinematic signatures in a cloud can result from a variety of phenomena like expanding H II regions, powerfull stellar winds, supernova explosions, outflows, magnetic fields, or even from simple solid-body rotation or galactic shear. For example, the morphology of the $\rho$ Oph complex (Vrba 1977; Loren 1989) suggests that both shocks and magnetic fields are the main mechanisms responsible for the elongation of the dark clouds L1709, L1755, L1729, and L1689N. These clouds are long filaments extending from the star-forming cores in $\rho$ Oph, and are aligned along a direction pointing toward the Upper-Scorpius (hereafter USco) subgroup of the Sco OB2 association (Loren 1989). External forces, such as an expanding supernova remnant or H II shell, applied to a gas complex can accelerate different clump masses at different rates. Differential acceleration can stretch a cloud into an elongated filament with the most massive component closest to the source of the external force. As a result, a velocity gradient is expected to appear along the filament axis. On the other hand, if different mass elements along a filament's length have the same $V_{\rm LSR}$, then it is evidence for there being no component of external force along the line of sight. Finally, while any differences in $V_{\rm LSR}$ from one end of a filament to the other are most likely not the result of rotation, transverse gradients are more likely to be the result of large-scale rotation (Goodman et al. 1993). Thus, studies of the velocity fields within molecular clouds are of crucial importance in order to characterize the dynamical state of the clouds.

The extensive velocity information contained in spectral-line maps provides the opportunity to analyse motions in molecular clouds carefully, and thus to estimate accurately the magnitude and direction of the velocity gradients, if present. The CO and ¹³CO lines are a useful probe of the large-scale velocity field in a cloud because of its widespread detectability, but are not an unbiased probe in all cases, due to opacity effects. In the case of GF 20, we have decided to use the CO line as a probe because the lines are gaussian in shape and narrow ( $\Delta v\sim0.9$ km s^-1). For GF 17, we selected the ¹³CO line because the CO line was found to be very assymetric and broad ( $\Delta v\sim1.3$ km s^-1) toward most lines-of-sight. Nevertheless, it is extremely unlikely that our velocity gradient calculations will be significantly affected by opacity effects because narrow linewidths do not allow large errors in velocity, even for lines-of-sight with large optical depths. Although available for fewer positions, the C¹⁸O data was also used to probe the kinematic signatures that may exist within the denser regions.

Figure 15: Left panel: variation of the LSR central velocity of the 13CO line as function of right ascension offset in GF 17. Right panel: same plot but for the CO line in GF 20. The velocity resolutions are indicated in each panel. The vertical dashed lines separate the main core region from the filamentary region in each cloud. Note the systematic increase of the LSR velocities with right ascension offset away from position offsets $\Delta \alpha \sim 0^{\prime }$ in GF 17 and $\Delta \alpha \sim -8^{\prime }$ in GF 20.

In Fig. 15, the LSR central velocity of the ¹³CO (GF 17) and CO (GF 20) lines is plotted against right ascension offset from the reference map positions. The velocity resolutions are 0.12 km s^-1 for CO (in GF 17) and 0.11 km s^-1 for ¹³CO (in GF 20). The vertical dashed lines separate the main core region from the filamentary region in each cloud. A striking dependence (over ${\sim}40^{\prime}$ in right ascension offset in both clouds) of line velocity with position is clearly seen. We focus our analysis on the following remarks:

1.

We find a systematic, smooth increase of the LSR velocities away from position offsets $\Delta \alpha \sim 0^{\prime }$ in GF 17 and $\Delta \alpha \sim -8^{\prime }$ in GF 20. These position offsets correspond to the lowest LSR velocities, respectively $V_{\rm LSR}\sim+3.9$ km s^-1 and $V_{\rm LSR}\sim+4.5$ km s^-1, observed toward GF 17 and GF 20, respectively. The line velocities in GF 17 increase smoothly to $V_{\rm LSR}\sim+4.4$ km s^-1 (at $\Delta \alpha\sim-10^{\prime}$) toward the west, and to $V_{\rm LSR}\sim+4.3$ km s^-1 (at $\Delta \alpha\sim+30^{\prime}$) toward the east. For GF 20, the line velocities increase continuously to $V_{\rm LSR}\sim+5.2$ km s^-1 in both directions.

2.

There appears to be an abrupt jump in $V_{\rm LSR}$ (from ${\sim}$+4.1 km s^-1 to ${\sim}$+4.6 km s^-1) occuring at the position offset $\Delta \alpha\sim+10^{\prime}$. This region corresponds to the dense core located just about $6^{\prime}$ to the northeast of the main core region seen in Fig. 1. We interpret this dense core as a dynamically single unit within GF 17. However, note that this shift in velocity is smaller than the typical ¹³CO line width in GF 17, implying that if GF 17 was at a greater distance, it would be misinterpreted as a larger internal clump turbulence.

3.

The dispersion in LSR velocities at each right ascension offset is generally larger in GF 17 than in GF 20. The filamentary region of GF 17 has larger velocity dispersions than the main core region, while the opposite is true for GF 20. In this cloud, the difference in velocity dispersions is partly due to the fact the lines are nearly gaussian in the filamentary region, but very assymetric in the main core region (owing to several blended velocity components along the line-of-sight, Moreira & Yun 2002). For GF 17, the spectral lines toward the eastern half of main core region are made of two distinct, resolved velocity components, so that we have plotted in Fig. 15 only the stronger (blue-shifted) component. Also, note that the velocity dispersion observed at each right ascension offset is also a natural consequence of there being a dependence of the velocity gradient with declination offset.

4.

In both clouds, the line velocities appear to become roughly constant (more evident in GF 20) at the eastern edge of the mapped region, while at the western edge $V_{\rm LSR}$ may well increase farther away to the west. In order to check if the velocity gradients could be traced outside our mapped regions, we have obtained additional CO and ¹³CO spectra within GF 17 and GF 20, but outside the regions presented here. It turns out that $V_{\rm LSR}\sim+5$ km s^-1 at $\Delta \alpha\sim+75^{\prime}$, and $V_{\rm LSR}\sim+4.6$ km s^-1 at $\Delta \alpha\sim-25^{\prime}$ for GF 17. Within GF 20, we find $V_{\rm LSR}\sim+5.7$ km s^-1 at $\Delta \alpha\sim+40^{\prime}$ and $V_{\rm LSR}\sim+4.9$ km s^-1 at $\Delta \alpha\sim-30^{\prime}$. Thus, the trend of increasing velocity in GF 17 can be traced far beyond the mapped region, and in GF 20 the same trend can be traced to the east, while the LSR velocities appear to become more constant to the west.

5.

The general behaviour depicted in Fig. 15 is well reproduced if we use instead the C¹⁸O maps of GF 17 and GF 20. This implies that our calculations of the velocity gradients are not significantly affected by opacity effects in the CO and ¹³CO lines. The magnitude of the velocity gradients obtained here for GF 17 and GF 20 are typically 2 to 3 times larger than the previous estimates by Vilas-Boas et al. (2000).

From the considerations above, we conclude that the overall velocity gradient structure in GF 17 and GF 20 is remarkably similar (both morphologically and spatially), strongly suggesting a common origin. In order to investigate the origin of such velocity gradients, we need a quantitative analysis of the velocity structures of these clouds. We fit the CO, ¹³CO, and C¹⁸O maps of line-center velocity using a least-squares technique for the true direction and magnitude of the best-fit velocity gradient. The velocity, $V_{\rm LSR}$, at the peak of a symmetric emission profile is assumed to represent an intensity-weighted average velocity along the line of sight through the cloud.

If the cloud producing the emission line rotates as a solid body, $V_{\rm LSR}$ will be independent of distance along the line of sight, and linearly dependent on the coordinates in the plane of the sky (Goodman et al. 1993). Thus a cloud undergoing solid-body rotation can be expected to exhibit a linear gradient, $\nabla V_{\rm LSR}$, across the face of a map, perpendicular to the rotation axis. We fit the function $V_{\rm LSR} = V_{0} + a\Delta\alpha + b\Delta\delta$ to the data, where $\Delta\alpha$ and  $\Delta\delta$ represent offsets in right ascension and declination, expressed in radians, a and b are the projections of the gradient per radian on the $\alpha$ and $\delta$ axes, and V₀ is the systemic velocity of the cloud, with respect to the local standard of rest. The magnitude of the velocity gradient, in a cloud at distance D, is then given by $\nabla V_{\rm LSR}=(a^{2}+b^{2})^{1/2}/D$ and its direction (the direction of increasing velocity, measured east of north) is given by $\theta={\rm tan}^{-1}(a/b)$. From this, we can estimate the amount of solid-body rotation implied by the observed line of sight velocity field in a cloud. However, note that rotation is only one possible interpretation for any gradient found.

We have used the routine by Goodman et al. (1993), which performs a least-squares fit to the velocity field observed in a spectral-line map of a molecular cloud, and returns the magnitude of the gradient, its direction, and the errors in those quantities. Each observed value of $V_{\rm LSR}$ is weighted by $1/\sigma_{V}^{2}$, where $\sigma_{V}$ is the uncertainty in $V_{\rm LSR}$ determined by a Gaussian fit to the line profile. Fitting all ¹³CO data points in GF 17, we find a best-fit velocity gradient of ${\sim}0.46$ km s^-1 pc^-1 with direction $\theta=145^{\circ}$ east of north; fitting all the C¹⁸O data, one obtains the same magnitude for the best-fit velocity gradient and a slightly different direction, $\theta=154^{\circ}$. For GF 20, the CO best-fit velocity gradient is ${\sim}1.0$ km s^-1 pc^-1 with direction $\theta=134^{\circ}$, again in good agreement with the values derived from all the C¹⁸O data ( $\nabla V_{\rm LSR}=0.76$ km s^-1 pc^-1 and $\theta=127^{\circ}$). To estimate the significance of our derived velocity gradients, we calculate the ratio $\nabla V_{\rm LSR}/3\sigma$, where $\sigma$ is the error in the fitted velocity gradient. We find ratios of 267 and 16 for ¹³CO and C¹⁸O, respectively, in GF 17, and 667 and 24 for CO and C¹⁸O, respectively, in GF 20. Thus, our best-fit velocity gradients are very robust.

Considering the plane-of-the-sky orientation of GF 20, we conclude that the overall velocity gradients found are roughly perpendicular to the major axis of the filamentary structure. In principle, this could be interpreted as large-scale rotation of the cloud about its major axis. However, in this case a linear dependence of $V_{\rm LSR}$ along the full extent of the cloud would be expected. As shown in Fig. 15, this is not the case since the sense of the increase in $V_{\rm LSR}$ within the main core region does not coincide with that found for the filamentary region. To better analyze the kinematic differences between the filamentary regions and the main core regions of GF 17 and GF20, we have calculated best-fit velocity gradients within those regions separately. The results are listed in Table 2. Clearly, the velocity gradients within the main core regions and those within the filamentary regions exhibit different plane-of-the-sky orientations, but also differ in magnitude (typically a factor 2-2.5 larger in the main core regions). Caution should be taken in interpreting the velocity shifts in the main core regions as simple streaming motions, because as mentioned above (1) these regions exhibit possibly several blended velocity components, and (2) the observed changes in velocity in those regions are comparable or smaller than the CO and ¹³CO line widths therein, suggesting that we may be witnessing changes in the relative strength of different components along the line of sight. In any case, comparing the filamentary regions or the main core regions in both clouds, we find very similar magnitudes of the best-fit velocity gradients. We also note that the directions of the best-fit velocity gradients in the main core regions are remarkably similar. Taken together, these results argue that simple large-scale rotation cannot account for the velocity gradients and their similarities in GF 17 and GF 20, and instead strongly suggest a more complex, common origin.

 

 

Table 2: Results of gradient fitting.

Cloud	Region	Gradient	Direction	Gradient	Number of	Region
		(km s-1 pc-1)	(deg E of N)	significance	points in fit	of fit
		CO
GF 20	filament	0.48	40	180	397	$\Delta \alpha>-8^{\prime}$
	main core	1.22	-83	392	132	$\Delta \alpha<-8^{\prime}$
		13CO
GF 17	filament	0.39	94	288	288	$\Delta \alpha>0^{\prime}$
	main core	0.80	-80	47	80	$\Delta \alpha<0^{\prime}$
		C18O
GF 17	filament	0.66	63	23	108	$\Delta \alpha>0^{\prime}$
	main core	1.63	-132	21	26	$\Delta \alpha<0^{\prime}$
GF 20	filament	0.30	153	7	264	$\Delta \alpha>-8^{\prime}$
	main core	2.29	-157	9	9	$\Delta \alpha<-8^{\prime}$

Could galactic shear produce such velocity gradients? It seems very unlikely because the overall best-fit velocity gradients in GF 17 and GF 20 given above are nearly perpendicular to the galactic plane. Still, we can estimate the inclination to the plane of the sky of GF 17 and GF 20 which is required so that the velocity gradient induced by galactic shear reproduces the velocity gradients observed. The velocity gradient induced in a cloud with galactic longitude, l, at an inclination angle, i, to the plane-of-the-sky is given by $\Delta v=A\sin(2l)$tan(i)$\Delta r$, where A is the Oort A constant and $\Delta r$ is the offset position across the face of the cloud map. From Fig. 15 we take $\Delta v=0.8$ km s^-1, corresponding to the velocity shift observed across ${\sim}27^{\prime}$ (or about $\Delta r=1.2$ pc) along the filamentary regions of GF 17 or GF 20. Using A=16 km s^-1 kpc^-1 (Mihalas & Binney 1981), we derive $i\sim86^{\circ}$. Then, if galactic shear is the dominant mechanism producing the observed velocity gradient, this requires that GF 17 and GF 20 be nearly perpendicular to the plane-of-the-sky, i.e. along the line-of-sight. This seems very unlikely because it would imply that the true extent of the filamentary regions in GF 17 and GF 20 would have to be of the order of ${\sim}17$ pc, that is to say of the order of the diameter of the whole Lupus complex of dark clouds. Furthermore, these clouds appear to be small and dense, and thus insusceptible to the effects of a differential gravitational field. Thus, the velocity structures of GF 17 and GF 20 were likely produced by some mechanism other than galactic shear or simple large-scale rotation. We discuss the nature of such mechanism in Sect. 5.2.