A Salpeter-like filament linear density function across nearby molecular clouds

Abstract

The high-mass slope of the stellar initial mass function (IMF), first measured by Salpeter in 1955, appears nearly universal across star-forming environments, yet its physical origin remains unknown. Using the multiscale extraction method getsf, we measure the filament linear density function (FLDF) across seven nearby molecular clouds ($140-920$ pc) spanning a wide range of star-forming activity. The scale-dependent FLDF steepens systematically from shallow slopes on small spatial scales to a Salpeter-like slope on the largest scale. When integrated over the full hierarchy of scales, the composite FLDF follows a power law ${\rm d}N/{\rm d}\logΛ\propto Λ^{-α}$ with $α\approx 1.30-1.34$, indistinguishable from the Salpeter value of $1.35$, and this composite slope is the same across all clouds despite an order-of-magnitude spread in their supercritical-filament fractions. The universal stellar mass spectrum thus appears to be encoded already in the hierarchical filamentary structure of the cold interstellar medium.