Context : Converging networks of interstellar filaments , i.e .
hubs , have been recently linked to the formation of stellar clusters and massive stars .
Understanding the relationship between the evolution of these systems and the formation of cores/stars inside them is at the heart of current star formation research .

Aims : The goal is to study the kinematic and density structure of the SDC13 prototypical hub at high angular resolution to determine what drives its evolution and fragmentation .

Methods : We have mapped SDC13 , a \sim 1000 M _ { \odot } infrared dark hub , in NH _ { 3 } ( 1,1 ) and NH _ { 3 } ( 2,2 ) emission lines , with both the Jansky Very Large Array and Green Bank Telescope .
The high angular resolution achieved in the combined dataset allowed us to probe scales down to 0.07pc .
After fitting the ammonia lines , we computed the integrated intensities , centroid velocities and line widths , along with gas temperatures and H _ { 2 } column densities .

Results : The mass-per-unit-lengths of all four hub filaments are thermally super-critical , consistent with the presence of tens of gravitationally bound cores identified along them .
These cores exhibit a regular separation of \sim 0.37 \pm 0.16 pc suggesting gravitational instabilities running along these super-critical filaments are responsible for their fragmentation .
The observed local increase of the dense gas velocity dispersion towards starless cores is believed to be a consequence of such fragmentation process .
Using energy conservation arguments , we estimate that the gravitational to kinetic energy conversion efficiency in the SDC13 cores is \sim 35 \% .
We see velocity gradient peaks towards \sim 63 \% of the cores as expected during the early stages of filament fragmentation .
Another clear observational signature is the presence of the most massive cores at the filaments ’ junction , where the velocity dispersion is the largest .
We interpret this as the result of the hub morphology generating the largest acceleration gradients near the hub centre .

Conclusions : We propose a scenario for the evolution of the SDC13 hub in which filaments first form as post-shock structures in a supersonic turbulent flow .
As a result of the turbulent energy dissipation in the shock , the dense gas within the filaments is initially mostly sub-sonic .
Then gravity takes over and starts shaping the evolution of the hub , both fragmenting filaments and pulling the gas towards the centre of the gravitational well .
By doing so , gravitational energy is converted into kinetic energy in both local ( cores ) and global ( hub centre ) potential well minima .
Furthermore , the generation of larger gravitational acceleration gradients at the filament junctions promotes the formation of more massive cores .