  In order to shed light on the main physical processes controlling
fragmentation of massive dense cores, we present a uniform study of the density
structure of 19 massive dense cores, selected to be at similar evolutionary
stages, for which their relative fragmentation level was assessed in a previous
work. We inferred the density structure of the 19 cores through a simultaneous
fit of the radial intensity profiles at 450 and 850 micron (or 1.2 mm in two
cases) and the Spectral Energy Distribution, assuming spherical symmetry and
that the density and temperature of the cores decrease with radius following
power-laws. We find a weak (inverse) trend of fragmentation level and density
power-law index, with steeper density profiles tending to show lower
fragmentation, and vice versa. In addition, we find a trend of fragmentation
increasing with density within a given radius, which arises from a combination
of flat density profile and high central density and is consistent with Jeans
fragmentation. We considered the effects of rotational-to-gravitational energy
ratio, non-thermal velocity dispersion, and turbulence mode on the density
structure of the cores, and found that compressive turbulence seems to yield
higher central densities. Finally, a possible explanation for the origin of
cores with concentrated density profiles, which are the cores showing no
fragmentation, could be related with a strong magnetic field, consistent with
the outcome of radiation magnetohydrodynamic simulations.
