How the power spectrum of dust continuum images may hide the presence of a characteristic filament width

Context. Herschel observations of interstellar clouds support a paradigm for star formation in which molecular filaments play a central role. One of the foundations of this paradigm is the finding, based on detailed studies of the transverse column density profiles observed with Herschel, that nearby molecular filaments share a common inner width of ∼0.1 pc. The existence of a characteristic filament width has been recently questioned, however, on the grounds that it seems inconsistent with the scale-free nature of the power spectrum of interstellar cloud images. Aims. In an effort to clarify the origin of this apparent discrepancy, we examined the power spectra of the Herschel/SPIRE 250 μm images of the Polaris, Aquila, and Taurus–L1495 clouds in detail and performed a number of simple numerical experiments by injecting synthetic filaments in both the Herschel images and synthetic background images. Methods. We constructed several populations of synthetic filaments of 0.1 pc width with realistic area filling factors (Afil) and distributions of column density contrasts (δc). After adding synthetic filaments to the original Herschel images, we recomputed the image power spectra and compared the results with the original, essentially scale-free power spectra. We used the χ2variance of the residuals between the best power-law fit and the output power spectrum in each simulation as a diagnostic of the presence (or absence) of a significant departure from a scale-free power spectrum. Results. We find that χ2variance depends primarily on the combined parameter δ22 Afil. According to our numerical experiments, a significant departure from a scale-free behavior and thus the presence of a characteristic filament width become detectable in the power spectrum when δ22 Afil ⪆ 0.1 for synthetic filaments with Gaussian profiles and δ22 Afil ⪆ 0.4 for synthetic filaments with Plummer-like density profiles. Analysis of the real Herschel 250 μm data suggests that δ22 Afil is ∼0.01 in the case of the Polaris cloud and ∼0.016 in the Aquila cloud, significantly below the fiducial detection limit of δ22 Afil ∼ 0.1 in both cases. In both clouds, the observed filament contrasts and area filling factors are such that the filamentary structure contributes only ∼1/5 of the power in the image power spectrum at angular frequencies where an effect of the characteristic filament width is expected. Conclusions. We conclude that the essentially scale-free power spectra of Herschel images remain consistent with the existence of a characteristic filament width ∼0.1 pc and do not invalidate the conclusions drawn from studies of the filament profiles.