  In order to study the fragmentation of massive dense cores, which constitute
the cluster cradles, we observed with the PdBI in the most extended
configuration the continuum at 1.3 mm and the CO(2-1) emission of four massive
cores. We detect dust condensations down to ~0.3 Msun and separate millimeter
sources down to 0.4" or ~1000 AU, comparable to the sensitivities and
separations reached in optical/infrared studies of clusters. The CO(2-1) high
angular resolution images reveal high-velocity knots usually aligned with
previously known outflow directions. This, in combination with additional cores
from the literature observed at similar mass sensitivity and spatial
resolution, allowed us to build a sample of 18 protoclusters with luminosities
spanning 3 orders of magnitude. Among the 18 regions, ~30% show no signs of
fragmentation, while 50% split up into ~4 millimeter sources. We compiled a
list of properties for the 18 massive dense cores, such as bolometric
luminosity, total mass, and mean density, and found no correlation of any of
these parameters with the fragmentation level. In order to investigate the
combined effects of magnetic field, radiative feedback and turbulence in the
fragmentation process, we compared our observations to radiation
magneto-hydrodynamic simulations, and found that the low-fragmented regions are
well reproduced in the magnetized core case, while the highly-fragmented
regions are consistent with cores where turbulence dominates over the magnetic
field. Overall, our study suggests that the fragmentation in massive dense
cores could be determined by the initial magnetic field/turbulence balance in
each particular core.
