5 Discussion

5.1 The source of dust heating

The presence of extended far-infrared emission in these cold clouds poses several problems; first, what is the heating source for the dust in these clouds? Second, can a sufficient fraction of dust mass be heated to produce the observed intensity in the far-infrared? Both the absence of luminous embedded sources in these clouds and the observed gradient in dust temperature suggest that the dust heating must be external to these clouds. One possible source of heating is the low-luminosity stars which have formed within GF 17 and GF 20. However, the total luminosities of the populations of T Tauri stars associated with GF 17 and GF 20 amount to ${\sim}4.6\,L_{\odot}$ and ${\sim}5.8\,L_{\odot}$, respectively (Krautter 1991; Hughes et al. 1994). From the total luminosities calculated above we find that the T Tauri populations can only account for $20\%$ of the far-infrared luminosity in GF 17 and GF 20. Thus, the young low-mass stars associated with GF 17 and GF 20 cannot be the dominant source of dust heating in these clouds.

A likely candidate for the heat source then is the interstellar radiation field (ISRF). Both Mathis et al. (1983) and de Muizon & Rouan (1985) have computed models of interstellar clouds heated by a standard ISRF. Both studies found that the mean temperature of grains exposed to the standard ISRF is 10 K for silicate grains and 20 K for graphite grains (see also Draine & Lee 1984), smaller than the average temperature of the grains responsible for the emission in our clouds. From the model calculations of Spencer & Leung (1978), we find that the ratio of flux densities at 60 and $100~\mu$m should be approximately 0.55 for graphite grains and approximately 0.03 for silicate grains. The observed flux density ratio in our clouds range from 0.16 to 0.30; if the intensity of the ISRF is uniform, then our clouds must contain a mixture of the two types of grains. The fact that our calculated temperatures are significantly higher than 20 K indicates that if the ISRF is the dominant source of dust heating, then this ISRF has to be particularly intense near GF 17 and GF 20, as is the case in the $\rho$ Oph complex.

This led us to investigate the possibility that the nearby Sco OB2 association is responsible for the high dust temperatures found within GF 17 and GF 20. Like the $\rho$ Oph cloud, the Lupus clouds lie close to the Upper-Scorpius (hereafter USco) subgroup ($D\sim170$ pc) of the Sco OB2 association (Murphy et al. 1986). The stars in USco that lie close to $\rho$ Oph contribute approximately $1000~L_{\odot}$ (Ryter et al. 1987; de Geus et al. 1989) by irradiating the cloud's surface (approximately 10 pc²) with an absorbed flux of about $5\times10^{-2}$ erg s^-1 cm^-2. It is difficult to assess the three-dimensional configuration of GF 17, GF 20, and $\rho$ Oph relative to the USco subgroup. Still, we can make a rough estimate of the contribution of the OB2 association to the far-infrared luminosities of GF 17 and GF 20. The surface areas contained in our molecular maps of GF 17 and GF 20 are 0.32 pc² and 0.36 pc², respectively. Assuming that the true distance from the USco association to each one of the clouds is simply the projected distance on the plane of the sky, one finds that GF 20 and GF 17 are, respectively, roughly 2.5 and 3.3 times more distant to USco than the $\rho$ Oph cloud. This translates into absorbed fluxes of ${\sim}4.6\times10^{-3}$ and ${\sim}8.0\times10^{-3}$ erg s^-1 cm^-2 for GF 17 and GF 20, yielding far-infrared luminosities of $3.7~L_{\odot}$ and $7.2~L_{\odot}$. These values are in excellent agreement with the far-infrared luminosities derived above from our IRAS images, given the uncertainties. Therefore, contributions to the far-infrared luminosities of these clouds from unknown external or hidden internal sources must be minimal, and we conclude that the dominant source of dust heating in GF 17 and GF 20 is likely to be the ISRF due to the Sco OB2 association.

   
5.2 The origin of the cloud structures

The interaction between the $\rho$ Oph cloud complex and the USco association is well established (Olano & Pöppel 1981; Cappa de Nicolau & Pöppel 1986; Ryter et al. 1987; de Geus et al. 1989; Loren 1989; de Geus et al. 1990; Nozawa et al. 1991; de Geus 1992). The star formation efficiency (SFE) in $\rho$ Oph is very high ( ${\sim}20\%$), while it is only of the order of $0.3\%$ in the Ophiuchus north region. Nozawa et al. (1991) suggested that such low SFE could be attributed to the high ionization degree due to the strong UV radiation field from the Sco OB2 association, which could prevent the molecular clouds therein from collapsing via strong coupling between magnetic fields and the molecular gas. More recently, Tachihara et al. (1996) found that the SFE in GF 20 is ${\sim}0.9\%$, while in Lupus 1 ( ${\sim}0.4\%$) it is comparable to that found by Nozawa et al. (1991) in the Ophiuchus north region. In Lupus 3, they found the SFE to be significantly higher ( ${\geq}3.8\%$). On the other hand, Hughes et al. (1994) showed that there is a large difference among the stellar ages associated with the dark clouds in Lupus. The T Tauri stars in Lupus 3 and GF 17 are on average much older (respectively ${\sim}7\times10^{6}$ yr and ${\sim}4\times10^{6}$ yr) than those in Lupus 1 ( ${\sim}8\times10^{5}$ yr) and GF 20 ( ${\sim}5\times10^{5}$ yr). Tachihara et al. (1996) interpreted these facts as an indication that star formation in Lupus 1 and GF 20 was triggered by the interaction with the giant HI expanding shell that surrounds the USco subgroup (Cappa de Nicolau & Pöppel 1986; de Geus 1992). Figure 5 in Tachihara et al. (1996) shows that the Lupus complex of dark clouds is seen in projection against the edge of the USco shell, indicating that GF 17 and GF 20 are likely to be affected by the expanding shell.

Figure 16: Distribution of observed radial velocities in GF 17 and GF 20 versus galactic latitude (filled squares). The crosses represent the distribution of radial velocities from HI data from the Upper-Scorpius shell. The solid lines represent the best-fit models by Cappa de Nicolau & Pöppel (1986) of an expanding shell with expansion velocity of 6 km s-1, centered at $(l,b)=(347^{\circ },+22^{\circ })$, and with a systemic velocity of 2 km s-1 (shown by the filled triangle). The dashed line represents the best-fit model by de Geus (1992) of an expanding shell with expansion velocity of 10 km s-1, centered at $(l,b)=(347^{\circ },+21^{\circ })$, and with a systemic velocity of 0 km s-1 (shown by the empty triangle). The short-long dashed line is the best-fit model by de Geus (1992) of the HI shell surrounding the Upper-Centaurus-Lupus subgroup, which expands at 10 km s-1; the Upper-Centaurus-Lupus shell is centered at $(l,b)=(320^{\circ },+10^{\circ })$, has a systemic velocity of ${\sim }1$ km s-1 (shown by the empty square).

This can also be seen in Fig. 16 were we plot the LSR velocities versus galactic latitude for every position in our molecular line maps of GF 17 and GF 20. Also plotted is the distribution of radial velocities from HI data (shown as crosses) from Heiles & Habing (1974), Pöppel et al. (1979), and Cappa de Nicolau & Pöppel (1986), collected both at the center ( $0 \leq V_{\rm lsr}\leq 4$ km s^-1) and edges ( $V_{\rm lsr}\sim-4$ km s^-1 and $V_{\rm lsr}\sim+8$ km s^-1) of the USco shell. The solid lines represent the best-fit model (Cappa de Nicolau & Pöppel 1986) of an expanding shell with expansion velocity of 6 km s^-1, for three different ratios of R/r₀, where the R is the radius of the shell and r₀ is the distance to the observer. Also shown (dashed line) is a best-fit model by de Geus (1992) of a shell with radius R=40 pc and expanding at a larger velocity (10 km s^-1), based on additional HI data in the USco and Ophiuchus regions from de Geus & Burton (1991). Both models clearly show that GF 17 and GF 20 are within or at the boundaries of the expanding USco shell. On the other hand, considering the galactic coordinates of our clouds, we note that GF 17 and GF 20 are located near the Upper-Centaurus-Lupus (hereafter UCen-Lup) association, the oldest subgroup of the Sco OB2 association (see Fig. 1b in de Geus 1992). A best-fit model (de Geus 1992) of the expanding HI shell surrounding the UCen-Lup subgroup is also plotted (short-long dashed line) in Fig. 16. Much larger ($R\sim110$ pc) than the USco shell, its expanding velocity is 10 km s^-1 with respect to its systemic velocity of ${\sim}0$ km s^-1. We note that the UCen-Lup shell encompasses the USco shell. Then, at the current expansion rate the UCen-Lup shell must have passed the USco region. Therefore, it is likely that the Lupus complex of dark clouds (including GF 17 and GF 20) was also shaped by the UCen-Lup shell.

From the present-day expansion rate and radius of the HI shells, de Geus (1992) estimated upper limits for their dynamical time scale, and found ${\sim}2.5\times10^{6}$ yr for the USco shell and ${\sim}11\times10^{6}$ yr for the UCen-Lup shell. From the relative positions of GF 17 and GF 20 with respect to the UCen-Lup shell (${\sim}42$ pc in the plane of the sky), we estimate that the shell must have passed the Lupus complex ${\sim}7\times10^{6}$ yr ago. However, note that an inclination of $60^{\circ}$ to the plane of the sky can lower this estimate to about ${\sim}3.5\times10^{6}$ yr, consistent with the estimate by de Geus (1992) that the UCen-Lup shell has passed the region of Upper-Scorpius about $4\times10^{6}$ yr ago. Thus, at the epoch when the USco shell was blown, the UCen-Lup shell was already passing through and compressing the Lupus clouds via the propagating shock front. From these numbers and the age of the T Tauri stars in the different Lupus clouds given above, and from the median age of the T Tauri stars in Lupus ( ${\sim}3.2\times10^{6}$ yr, Hughes et al. 1994, we conclude that it is possible that most of the T Tauri stars in Lupus 3 and GF 17 were formed due to the interaction with the UCen-Lup shell, and not with the USco shell. Apparently, at that time the Lupus 1 and GF 20 clouds were not dense enough to form stars since in these clouds almost all T Tauri stars are $1\times10^{6}$ yr old or less (Hughes et al. 1994). The recent star formation in Lupus 1 and GF 20 was likely induced by the USco shell (Tachihara et al. 1996).

Can we find observational evidence that GF 17 and GF 20 were shaped by both shells, and not only by the USco shell as proposed by Tachihara et al. (1996)? In spite of the obvious difficulty in assessing the 3 dimensional configuration (including distances) of the Lupus clouds with respect to the expanding shells, this seems to be the case, if we take into consideration (1) the close correspondence between the age of the USco shell and the time when the UCen-Lup shell passed the Lupus region, and (2) the present-day morphology and gas kinematics of GF 17 and GF 20. The velocity gradients over the filamentary regions of GF 17 and GF 20 impose upper limits to the cloud crossing times, which we find to be ${\sim}3\times10^{6}$ yr and ${\sim}2\times10^{6}$ yr, respectively, consistent with the time scales given above.

Moreover, the C¹⁸O velocity gradient observed along the filamentary region of GF 17 is aligned (within $5^{\circ}$) with the direction to, and away from the center of the UCen-Lup shell. Also, the CO velocity gradient in the filamentary region of GF 20 is also aligned, within $5^{\circ}$, with the direction toward the UCen-Lup shell, and points away from the shell. From a morphological point of view, GF 17 (which extends well beyond the region studied here) is closely aligned with the direction pointing toward the center of the UCen-Lup shell, and a similar behaviour is seen for GF 20; this is also the case of the Lupus 3 cloud (Tachihara et al. 1996). Finally, we note that the sense of increasing velocity (inferred from the positions of GF 17 and GF 20 in the LSR velocity-galactic latitude diagram in Fig. 16, which are located symmetrically with respect to the semi-minor velocity axis of the UCen-Lup shell) follows reasonably well the directions pointing away from the center (shown as an empty square) of the UCen-Lup shell, and not from the center of the USco shell, for either model shown. Thus, it seems plausible that the velocity gradients along the filamentary regions of GF 17 and GF 20 were originated by the interaction with the UCen-Lup shell.

On the other hand, considering the galactic coordinates of GF 20, we point out that the elongated main core region south of the T Tauri star RU Lupi points away from the center of the USco shell. Considering all positions within GF 17 and GF 20, the best-fit velocity gradients point away (within $20^{\circ}$) from the center of the USco shell. If the velocity gradients found in the main core regions of GF 17 and GF 20 represent bona fide large-scale streaming motions, their dynamical time scale is typically smaller than their counterparts in the filamentary regions by a factor of 2, suggesting that perhaps they did not originate from the interaction with the UCen-Lup shell, but instead were produced by the interaction with the more recent USco shell event. Taken together this facts seem to indicate that the swept-up appearance of GF 17 and GF 20 is likely due to the interaction with both the UCen-Lup and the USco shells, and not the USco shell alone.