Context : Exploring the structure and dynamics of cold starless clouds is necessary to understand the different steps leading to the formation of protostars .
Because clouds evolve slowly , many of them must be studied in detail to pick up different moments of a cloud ’ s lifetime .

Aims : We study here a fragment of the long filament L1506 in the Taurus region which we name L1506C , a core with interesting dust properties which have been evidenced with the PRONAOS balloon-borne telescope .

Methods : To trace the mass content of L1506C and its kinematics , we mapped the dust emission , and the line emission of two key species , C ^ { 18 } O and N _ { 2 } H ^ { + } . ^ { 13 } CO and C ^ { 17 } O were also observed .
We model the species emission using 1D Monte Carlo models .

Results : This cloud is reminiscent of L1498 but also shows peculiar features : i ) a large envelope traced solely by ^ { 13 } CO holding a much smaller core with a strong C ^ { 18 } O depletion in its center despite a low maximum opacity ( A _ { \mathrm { V } } \sim 20 mag ) , ii ) extremely narrow C ^ { 18 } O lines indicating a low , non-measurable turbulence , iii ) contraction traced by C ^ { 18 } O itself ( plus rotation ) , iv ) unexpectedly , the kinematical signature from the external envelope is opposite to the core one : the ^ { 13 } CO and C ^ { 18 } O velocity gradients have opposite directions and the C ^ { 18 } O line profile is blue peaked on the contrary to the ^ { 13 } CO one which is red peaked .
The core is large ( r = 3 \times 10 ^ { 4 } A.U . )
and not very dense ( n ( H _ { 2 } ) \leq 5 \times 10 ^ { 4 } cm ^ { -3 } , possibly less ) .
This core is therefore not prestellar yet .

Conclusions : All these facts suggest that the core is kinematically detached from its envelope and in the process of forming a prestellar core .
This is the first time that the dynamical formation of a prestellar core is witnessed .
The extremely low turbulence could be the reason for the strong depletion of this core despite its relatively low density and opacity in contrast with undepleted cores such as L1521E which shows a turbulence at least 4 times as high .