Structure formation in a mixed dark matter model with decaying sterile
  neutrino: the 3.5 keV X-ray line and the Galactic substructure
  We perform a set of cosmological simulations of structure formation in a
mixed dark matter (MDM) model. Our model is motivated by the recently
identified $3.5\,{\rm keV}$ X-ray line, which can be explained by the decay of
non-resonantly produced sterile neutrinos accounting for $20$-$60\%$ of the
dark matter in the Universe. These non-resonantly produced sterile neutrinos
have a sizable free-streaming length and hence behave effectively as warm dark
matter (WDM). Assuming the rest of dark matter is composed of some cold dark
matter (CDM) particles, we follow the coevolution of a mixed WDM plus CDM
cosmology. Specifically, we consider the models with the warm component
fraction of $r_{\rm warm}=0.25$ and $0.50$. Our MDM models predict that the
comoving Jeans length at the matter-radiation equality is close to that of the
thermally produced warm dark matter model with particle mass $m_{\rm
WDM}=2.4\,{\rm keV}$, but the suppression in the fluctuation power spectrum is
weaker. We perform large $N$-body simulations to study the structure of
non-linear dark halos in the MDM models. The abundance of substructure is
significantly reduced in the MDM models, and hence the so-called small-scale
crisis is mitigated. The cumulative maximum circular velocity function (CVF) of
at least one halo in the MDM models is in good agreement with the CVFs of the
observed satellites in the Milky Way and the Andromeda galaxy. We argue that
the MDM models open an interesting possibility to reconcile the reported
$3.5\,{\rm keV}$ line and the internal structure of galaxies.
