The role of molecular filaments in the origin of the prestellar core mass function and stellar initial mass function

Context. The origin of the stellar initial mass function (IMF) is one of the most debated issues in astrophysics. Aims. Here we explore the possible link between the quasi-universal filamentary structure of star-forming molecular clouds and the origin of the IMF. Methods. Based on our recent comprehensive study of filament properties from Herschel Gould Belt survey observations, 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. Results. We find that the FMF and the FLMF have very similar shapes and are both consistent with a Salpeter-like power-law function (dN/dlog M-line proportional to M-line(-1.5 +/- 0.1)) in the regime of thermally supercritical filaments(M-line > 16 M-circle dot pc(-1)). 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 dN/dlog M-cl proportional to M-cl(-0.7). Conclusions. 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.