  The simplest way to create sterile neutrinos in the early Universe is by
their admixture to active neutrinos. However, this mechanism, connected to the
Dark Matter (DM) problem by Dodelson and Widrow (DW), cannot simultaneously
meet the relic abundance constraint as well as bounds from structure formation
and X-rays. Nonetheless, unless a symmetry forces active-sterile mixing to
vanish exactly, the DW mechanism will unavoidably affect the sterile neutrino
DM population created by any other production mechanism. We present a
semi-analytic approach to the DW mechanism acting on an arbitrary initial
abundance of sterile neutrinos, allowing to combine DW with any other preceding
production mechanism in a physical and precise way. While previous analyses
usually assumed that the spectra produced by DW and another mechanism can
simply be added, we use our semi-analytic results to discuss the validity of
this assumption and to quantify its accurateness, thereby also scrutinising the
DW spectrum and the derived mass bounds. We then map our results to the case of
sterile neutrino DM from the decay of a real SM singlet coupled to the Higgs.
Finally, we will investigate aspects of structure formation beyond the usual
simple free-streaming estimates in order to judge on the effects of the DW
modification on the sterile neutrino DM spectra generated by scalar decay.
