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Herschel observations of interstellar clouds support a paradigm for starformation in which filaments play a central role. One of the foundations ofthis paradigm is the finding, based on studies of the radial column densityprofiles, that nearby filaments share a common inner width of ~0.1 pc. Theexistence of a characteristic filament width has been questioned, however, asit seems inconsistent with the scale-free nature of the power spectrum of cloudimages.  In an effort to clarify the origin of this apparent discrepancy, we examinedthe power spectra of the Herschel 250 micron images of the Polaris, Aquila, andTaurus clouds and performed a number of simple numerical experiments byinjecting synthetic filaments in both the Herschel images and syntheticbackground images.  We constructed several populations of synthetic filaments of 0.1 pc widthwith realistic area filling factors ($A_{\rm fil}$) and distributions of columndensity contrasts ($\delta_c$). After adding synthetic filaments to theHerschel images, we re-computed the image power spectra and compared theresults with the original, essentially scale-free power spectra. We used the$\chi^2$ variance of the residuals between the best power-law fit and theoutput power spectrum as a diagnostic of the presence of a significantdeparture from a scale-free power spectrum.  We found that the $\chi^2$ variance depends primarily on the combinedparameter $\delta_c^2\, A_{\rm fil}$. Analysis of the real Herschel data showsthat the observed filamentary structure contributes only 1/5 of the power inthe power spectra at angular frequencies where an effect of the characteristicfilament width is expected.  We conclude that the scale-free power spectra of Herschel images remainconsistent with the existence of a characteristic filament width ~0.1 pc and donot invalidate the conclusions drawn from studies of the filament profiles.

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