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Figure 3: Composite 3-color images of the 11 deg2 Aquila field (left) and the 8 deg2 Polaris field (right) produced from our PACS/SPIRE parallel-mode images at 70, 160, and 500 m. The color coding of the Aquila image is such that Red = SPIRE 500 m, Green = PACS 160 m, Blue = PACS 70 m. For the Polaris image, Red = combination of the three SPIRE bands, Green = PACS 160 m, Blue = PACS 70 m. The Aquila composite image was also the first release of ``OSHI'', ESA's Online Showcase of Herschel Images (cf. http://oshi.esa.int and http://www.esa.int/SPECIALS/Herschel/SEMT0T9K73G_0.html).

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Figure 4: Mass vs. size diagrams for the starless cores detected with Herschel-SPIRE/PACS in Aquila ( left) and Polaris ( right) (blue triangles). The masses were derived as explained in Appendix A (see also Könyves et al. 2010) and the sizes were measured at 250 m. For reference, the locations of the (sub)mm continuum prestellar cores identified by Motte et al. 1998, 2001 in  Oph and NGC2068/2071, respectively, are shown, along with the correlation observed for diffuse CO clumps (shaded band - cf. Elmegreen & Falgarone 1996). The two black solid lines mark the loci of critically self-gravitating isothermal Bonnor-Ebert spheres at T = 7 K and T = 20 K, respectively. The 341 cores classified as prestellar by Könyves et al. (2010), out of a total of 541 starless cores in Aquila, are shown as filled triangles in the left panel. The 302 starless cores of Polaris lie much below the two Bonnor-Ebert lines in the right panel, suggesting they all are unbound. The red solid lines are two lines of constant mean column density at NH2 = 1021 cm-2 and NH2 = 1022 cm-2, respectively. The 5 detection threshold at d = 150 pc of existing ground-based (sub)mm (e.g., SCUBA) surveys as a function of size is shown by the dashed curve. (The shape of this curve reflects a constant sensitivity to column density until source size approaches the beam size). The 5 detection thresholds of our SPIRE 250 m observations, given the estimated levels of cirrus noise (cf. Sect. 2) and assumed distances of 260 pc for Aquila and 150 pc for Polaris, are shown by the blue curves. The blue arrow in the left panel indicates how the positions of the Herschel cores (and the blue curve marking the detection threshold) would move in the diagram if a distance of 400 pc were adopted for Aquila instead of 260 pc (see Appendix A).

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Appendix A: Derivation of core/filament properties and effects of distance uncertainties

As described in more detail in a companion paper by Könyves et al. (2010) on Aquila, the masses of the cores identified in the Herschel images with the getsources algorithm (see Men'shchikov et al. 2010) were derived by fitting grey-body functions to the spectral energy distributions (SEDs) constructed from the integrated flux densities measured with SPIRE/PACS for each core. We assumed the dust opacity law  cm²/g, where denotes frequency and is the dust opacity per unit (gas + dust) mass column density. This dust opacity law, which is very similar to that advocated by Hildebrand (1983), is consistent with the value  cm²/g adopted for starless cores in numerous earlier studies (e.g., Motte et al. 1998). Ignoring any systematic distance effect (see below), the core mass uncertainties are dominated by the uncertainty in , typically a factor of 2. Cores were classified as either protostellar or starless based on the presence or absence of significant PACS emission at 70 m, respectively (cf. Bontemps et al. 2010; Dunham et al. 2008). In the Polaris field, the cirrus noise level is so low (cf. Fig. 4-right) that we cannot exclude that a fraction of the 302 candidate starless cores extracted with getsources correspond to background galaxies.

A column density map was derived for each region from the Herschel images smoothed to the SPIRE 500 m resolution (36.9  FWHM) using a similar SED fitting procedure on a pixel by pixel basis (see, e.g., Figs. 1 and 6 of Könyves et al. 2010 for Aquila). To obtain the maps of the filamentary background shown in Fig. 1 of this paper, we then performed a ``morphological component analysis'' decomposition (e.g., Starck et al. 2003) of the original column density maps on curvelets and wavelets. The curvelet component images shown in Fig. 1 provide a good measurement of the column density distribution of the filamentary background after subtraction of the compact sources/cores since the latter are contained in the wavelet component. We estimate that these column density maps are accurate to within a factor of 2. The scaling in terms of the mass per unit length along the filaments is more uncertain, however, as it depends on distance (see below) and would in principle require a detailedanalysis of the radial profiles of the filaments, which is beyond the scope of the present letter. Here, we simply assumed that the filaments had a Gaussian radial column density profile and multiplied the surface density maps by , where W is the typical FWHM width of the filaments. We assumed a mean molecular weight of . At this stage, the correspondence between the critical line mass of the filaments, , and the visual extinction threshold, (see Sect. 4), is thus accurate to at best a factor of 2.

There is some ambiguity concerning the distance to the Aquila Rift region. A number of arguments, presented in a companion paper by Bontemps et al. (2010), suggest that the whole region corresponds to a coherent cloud complex at d_- = 260 pc (see also Gutermuth et al. 2008), which is the default distance adopted in the present paper for Aquila. However, other studies in the literature (see references in Bontemps et al. 2010) place the complex at a larger distance, d₊ = 400 pc. It is thus worth discussing briefly how our Aquila results would be affected if we adopted the larger distance estimate, d₊, instead of d_-. The core mass estimates, which scale as where is integrated flux density and is the Planck function, would systematically increase by a factor of 2.4. This would shift the CMF shown in Fig. 2-left to the right and thus lower the efficiency from 20-40% to 10-20%. In the mass versus size diagram of Fig. 4, the cores would move upward as indicated in the left panel of the figure, which would increase the fraction of candidate bound cores in Aquila from 63% to 81%. The column density map of the Aquila filaments shown in Fig. 1 would be unchanged, but the scaling in terms of the mass per unit length along the filaments would change by 50% upward, since the physical width of the filaments would increase by 50%. In other words, the highlighted regions in Fig. 1-left, where the mass per unit length of the filaments exceeds half the critical value, would slightly expand, increasing the contrast with the Polaris filaments and improving the correspondence between the spatial distribution of the prestellar cores/protostars in Aquila and that of the gravitationally unstable filaments. To summarize, our main conclusions do not depend strongly on the adopted distance.