We investigate galaxy formation in models with dark matter (DM) constituted by sterile neutrinos. Given their large parameter space, defined by the combinations of sterile neutrino mass $m_{ u}$ and mixing parameter $sin^2(2theta)$ with active neutrinos, we focus on models with $m_{ u}=7$ keV, consistent with the tentative 3.5 keV line detected in several X-ray spectra of clusters and galaxies. We consider i) two resonant production models with $sin^2(2theta)=5,10^{-11}$ and $sin^2(2theta)=2,10^{-10}$, to cover the range of mixing parameter consistent with the 3.5 keV line; ii) two scalar-decay models, representative of the two possible cases characterizing such a scenario: a freeze-in and a freeze-out case. We also consider thermal Warm Dark Matter with particle mass $m_X=3$ keV. Using a semi-analytic model, we compare the predictions for the different DM scenarios with a wide set of observables. We find that comparing the predicted evolution of the stellar mass function, the abundance of satellites of Milky Way-like galaxies, and the global star formation history of galaxies with observations does not allow to disentangle the effects of the baryonic physics from those related to the different DM models. On the other hand, the distribution of the stellar-to-halo mass ratios, the abundance of faint galaxies in the UV luminosity function at $zgtrsim 6$, and the specific star formation and age distribution of local, low-mass galaxies constitute potential probes for the considered DM scenarios. We discuss how next observations with upcoming facilities will enable to rule out or to strongly support DM models based on sterile neutrinos.
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