The role of molecular filaments in the origin of the prestellar core
  mass function and stellar initial mass function
  The origin of the stellar initial mass function (IMF) is one of the most
debated issues in astrophysics.
  Here, we explore the possible link between the quasi-universal filamentary
structure of star-forming molecular clouds and the origin of the IMF.
  Based on our recent comprehensive study of filament properties from Herschel
Gould Belt survey observations (Arzoumanian et al.), we derive, for the first
time, a good estimate of the filament mass function (FMF) and filament line
mass function (FLMF) in nearby molecular clouds. We use the observed FLMF to
propose a simple toy model for the origin of the prestellar core mass function
(CMF), relying on gravitational fragmentation of thermally supercritical but
virialized filaments.
  We find that the FMF and the FLMF have very similar shapes and are both
consistent with a Salpeter-like power-law function (d$N$/dlog$M_{\rm line}
\propto M_{\rm line}^{-1.5\pm0.1}$) in the regime of thermally supercritical
filaments ($M_{\rm line} > 16\, M_\odot$/pc). This is a remarkable result
since, in contrast, the mass distribution of molecular clouds and clumps is
known to be significantly shallower than the Salpeter power-law IMF, with
d$N$/dlog$M_{\rm cl} \propto M_{\rm cl}^{-0.7}$.
  Since the vast majority of prestellar cores appear to form in thermally
transcritical or supercritical filaments, we suggest that the prestellar CMF
and by extension the stellar IMF are at least partly inherited from the FLMF
through gravitational fragmentation of individual filaments.
