We present and discuss the results of the Herschel Gould Belt survey observations in a ~11 deg^2 area of the Aquila molecular cloud complex at d~260 pc, imaged with the SPIRE/PACS cameras from 70 to 500 micron. We identify a complete sample of starless dense cores and embedded protostars in this region, and analyze their global properties and spatial distributions. We find a total of 651 starless cores, ~60% of which are gravitationally bound prestellar cores, and they will likely form stars in the future. We also detect 58 protostellar cores. The core mass function (CMF) derived for the prestellar cores is very similar in shape to the stellar initial mass function (IMF), supporting the earlier view that there is a close physical link between the IMF and the CMF. The global shift in mass scale observed between the CMF and the IMF is consistent with a typical star formation efficiency of ~40%. By comparing the numbers of starless cores to the number of young stellar objects, we estimate that the lifetime of prestellar cores is ~1 Myr. We find a strong correlation between the spatial distribution of prestellar cores and the densest filaments. About 90% of the Herschel-identified prestellar cores are located above a background column density corresponding to A_V~7, and ~75% of them lie within filamentary structures with supercritical masses per unit length >~16 M_sun/pc. These findings support a picture wherein the cores making up the peak of the CMF (and probably responsible for the base of the IMF) result primarily from the gravitational fragmentation of marginally supercritical filaments. Given that filaments appear to dominate the mass budget of dense gas at A_V>7, our findings also suggest that the physics of prestellar core formation within filaments is responsible for a characteristic efficiency SFR/M_dense ~5+-2 x 10^-8 yr^-1 for the star formation process in dense gas.
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