Non-thermal warm dark matter limits from small-scale structure

We present small-scale structure constraints on sterile dark matter produced from a heavy mediator particle, inspired by models of moduli decay. Dark matter particles produced through this mechanism can contribute to the entire dark matter energy density but the particles have a non-thermal phase-space distribution; however, we show that the resulting linear matter power spectra can be mapped to effective thermal-relic warm dark matter models. This production mechanism is therefore subject to warm dark matter constraints from small-scale structure as probed by ultra-faint dwarf galaxy abundances and strong gravitational lensing flux ratio statistics. We use the correspondence to thermal-relic models to derive a lower bound on the non-thermal particle mass of $107\ \mathrm{keV}$, at $95\%$ confidence. These are the first and most stringent constraints derived on sterile dark matter produced via the heavy mediator decay scenario we consider.