Context : Filamentary structures are common in molecular clouds .
Explaining how they fragment to dense cores is a missing step in understanding their role in star formation .

Aims : We perform a case study of whether low-mass filaments are close-to hydrostatic prior to their fragmentation , and whether their fragmentation agrees with gravitational fragmentation models .
For this , we study the \sim 6.5 pc long Musca molecular cloud that is an ideal candidate for a filament at an early stage of fragmentation .

Methods : We employ dust extinction mapping in conjunction with near-infrared JHK _ { \mathrm { S } } band data from the CTIO/NEWFIRM instrument , and 870 \mu m dust continuum emission data from the APEX/LABOCA instrument , to estimate column densities in Musca .
We use the data to identify fragments from the cloud and to determine the radial density distribution of its filamentary part .
We compare the cloud ’ s morphology with ^ { 13 } CO and C ^ { 18 } O line emission observed with the APEX/SHeFI instrument .

Results : The Musca cloud is pronouncedly fragmented at its ends , but harbours a remarkably well-defined , \sim 1.6 pc long filament in its Center region .
The line mass of the filament is 21-31 M _ { \odot } pc ^ { -1 } and FWHM 0.07 pc .
The radial profile of the filament can be fitted with a Plummer profile that has the power-index of 2.6 \pm 11 % , flatter than that of an infinite hydrostatic filament .
The profile can also be fitted with a hydrostatic cylinder truncated by external pressure .
These models imply a central density of \sim 5-10 \times 10 ^ { 4 } cm ^ { -3 } .
The fragments in the cloud have a mean separation of \sim 0.4 pc , in agreement with gravitational fragmentation .
These properties , together with the subsonic and velocity-coherent nature of the cloud , suggest a scenario in which an initially hydrostatic cloud is currently gravitationally fragmenting .
The fragmentation has started a few tenths of a Myr ago from the ends of the cloud , leaving its centre yet relatively non-fragmented , possibly because of gravitational focusing in a finite geometry .

Conclusions :