Characterizing the properties of nearby molecular filaments observed with Herschel

[Abridged] Molecular filaments have received special attention recently, thanks to new observational results on their properties. In particular, our early analysis of filament properties revealed a narrow distribution of median widths centered at a value of about 0.1 pc. Here, we extend and complement our initial study with the analysis of the filamentary structures observed in eight nearby molecular clouds. We use the column density maps derived from Herschel data and the DisPerSE algorithm to trace a network of filaments in each cloud. We build synthetic maps to assess the completeness limit of our extracted sample and validate our measurements. Our analysis yields a selected sample of 599 filaments with aspect ratios larger than 3 and column density contrasts larger than 0.3. We show that our sample is more than 95% complete for column density contrasts larger than 1, with only 5% of spurious detections. On average, more than 15% of the total gas mass in the clouds, and more than 80% of the dense gas mass, is found to be in the form of filaments, respectively. Analysis of the radial column density profiles of the 599 filaments indicates a narrow distribution of crest-averaged inner widths, with a median value of 0.10 pc and an interquartile range of 0.07 pc. In contrast, the filaments span wide ranges in length, central column density, column density contrast, and mass per unit length. The characteristic filament width is well resolved by Herschel observations, and a median value of 0.1 pc is consistently found using three distinct estimates based on (1) a direct measurement of the width at half power after background subtraction, as well as (2) Gaussian and (3) Plummer fits. The existence of a characteristic filament width is further supported by the presence of a tight correlation between mass per unit length and central column density for the observed filaments.