Structure formation in a mixed dark matter model with decaying sterile neutrino: the 3.5 keV X-ray line and the Galactic substructure

Abstract

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.