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tokens: have been considered (e.g. Lovell et al. 2014 ; Vogelsberger et al. 2016 ; Iršič et al. 2017b ; Robles et al. 2017 ), among which are the so-called warm dark matter models, where the corresponding particles have non-negligible thermal velocities. In particular, sterile neutrinos with masses of a few keV have been shown to be an interesting candidate for warm dark matter particles (e.g. Boyarsky, Iakubovskyi Ruchayskiy 2012 , and references therein). Moreover, the three sterile neutrino model, also known as the neutrino minimal standard model (νMSM), can also explain baryogenesis processes and neutrino oscillations (Boyarsky et al. 2012 , and references therein). Recently, sterile neutrinos have gained renewed attention following the apparent detections of a 3.5 keV X-ray line in several galaxy clusters as well as M31, and at the centre of the Milky Way (Boyarsky et al. 2014 ; Bulbul et al. 2014 ; Boyarsky et al. 2015 ); for a review see, e.g. Iakubovskyi ( 2014 ). However, sterile neutrino decay as a source of the line remains contentious (e.g. Anderson, Churazov Bregman 2015 ; Gu et al. 2015 ; Jeltema Profumo 2016 ). Recent results from the Hitomi collaboration (Aharonian et al. 2017 ) have ruled out an atomic transition as the origin of the 3.5 keV line, but a dark matter interpretation is still possible due to the different sensitivity of the Hitomi instrument to narrow (atomic) and broad lines. The 11σ detection of the 3.5 keV signal by NuStar (Neronov, Malyshev Eckert 2016 ) from a quiescent region of the sky and subsequent confirmation of this result with Chandra (Cappelluti et al. 2017 ) suggest that the line is not a statistical fluctuation nor an artefact of the XMM–Newton ’s instrumentation. It is therefore important to find complimentary probes of these models as well as supporting future X-ray observatory missions such as XARM and ATHENA that will provide still stronger X-ray constraints. Due to their appreciable thermal velocities at early times, warm dark matter particles free-stream out of density perturbations and are responsible therefore for a cut-off in the linear power spectrum and by extension in the formation of structures at small scales. The exact scale at which the suppression happens is strongly related to the dark matter particle production mechanism. For example, for 7 keV sterile neutrinos with a lepton asymmetry (defined in Section 3 ) much smaller or larger than L 6 = 8 this happens at the scale of progressively more massive dwarf galaxies (Lovell et al. 2016 ), while in a CDM model the suppression happens at much smaller scales. Quantifying the number of small mass structures is therefore an essential approach to distinguish among different dark matter models. For example, Kennedy et al. ( 2014 ) and Lovell et al. ( 2016 ) have used semi-analytic models to compare the abundance of luminous Milky Way satellites predicted by sterile neutrino dark matter models with the observed number of dwarf spheroidals, and