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

## TL;DR

This study investigates whether the apparent absence of a characteristic filament width in Herschel cloud images is due to the power spectrum's scale-free nature, finding that the filament width can be hidden yet still consistent with previous profile-based results.

## Contribution

The paper demonstrates that the scale-free power spectrum of Herschel images does not preclude the existence of a characteristic filament width of ~0.1 pc, reconciling different observational approaches.

## Key findings

- Filamentary structures contribute only 20% of the power at relevant scales.
- Synthetic filaments with realistic properties can be hidden in the power spectrum.
- The scale-free nature of the power spectrum does not invalidate the characteristic filament width.

## Abstract

Herschel observations of interstellar clouds support a paradigm for star formation in which filaments play a central role. One of the foundations of this paradigm is the finding, based on studies of the radial column density profiles, that nearby filaments share a common inner width of ~0.1 pc. The existence of a characteristic filament width has been questioned, however, as it seems inconsistent with the scale-free nature of the power spectrum of cloud images. In an effort to clarify the origin of this apparent discrepancy, we examined the power spectra of the Herschel 250 micron images of the Polaris, Aquila, and Taurus clouds and performed a number of simple numerical experiments by injecting synthetic filaments in both the Herschel images and synthetic background images. We constructed several populations of synthetic filaments of 0.1 pc width with realistic area filling factors ($A_{\rm fil}$) and distributions of column density contrasts ($\delta_c$). After adding synthetic filaments to the Herschel images, we re-computed the image power spectra and compared the results with the original, essentially scale-free power spectra. We used the $\chi^2$ variance of the residuals between the best power-law fit and the output power spectrum as a diagnostic of the presence of a significant departure from a scale-free power spectrum. We found that the $\chi^2$ variance depends primarily on the combined parameter $\delta_c^2\, A_{\rm fil}$. Analysis of the real Herschel data shows that the observed filamentary structure contributes only 1/5 of the power in the power spectra at angular frequencies where an effect of the characteristic filament width is expected. We conclude that the 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.