The high-mass slope of the stellar initial mass function (IMF), first measured by E. Salpeter in 1955, appears universal across star-forming environments. Its origin remains a central unsolved problem in astrophysics. Using getsf, we measure the filament linear density function (FLDF) − the mass-per-unit-length distribution of filaments − across seven nearby molecular clouds (140−920 pc) spanning a wide range of star-forming activity. When integrated over the full hierarchy of spatial scales, the composite FLDF follows a power law with slope α≈1.30−1.34, indistinguishable from Salpeter's value of 1.35. The universal stellar mass spectrum is therefore already encoded in the hierarchical filamentary structure of the cold interstellar medium, providing a physical basis for the IMF universality assumed throughout extragalactic and cosmological astrophysics.
@article{arxiv.2604.14093,
title = {A Salpeter-like filament linear density function across nearby molecular clouds},
author = {Guo-Yin Zhang and Alexander Men'shchikov and Jin-Zeng Li},
journal= {arXiv preprint arXiv:2604.14093},
year = {2026}
}