  It has been shown previously that the DM in galactic halos can be explained
by a self-gravitating system of massive keV fermions (`inos') in thermodynamic
equilibrium, and predicted the existence of a denser quantum core of inos
towards the center of galaxies. In this article we show that the inclusion of
self-interactions among the inos, modeled within a relativistic
mean-field-theory approach, allows the quantum core to become massive and
compact enough to explain the dynamics of the S-cluster stars closest to the
Milky Way's galactic center. The application of this model to other galaxies
such as large elliptical harboring massive central dark objects of $\sim 10^9
M_\odot$ is also investigated. We identify these interacting inos with sterile
right-handed neutrinos pertaining to minimal extensions of the Standard Model,
and calculate the corresponding total cross-section $\sigma$ within an
electroweak-like formalism to be compared with other observationally inferred
cross-section estimates. The coincidence of an ino mass range of few tens of
keV derived here only from the galactic structure, with the range obtained
independently from other astrophysical and cosmological constraints, points
towards an important role of the right-handed neutrinos in the cosmic
structure.
