On the applicability of approximations used in calculation of spectrum of Dark Matter particles produced in particle decays

TL;DR

This paper critically examines the approximations used in calculating the momentum spectrum of Warm Dark Matter particles produced via particle decays, highlighting the conditions under which these approximations are valid.

Contribution

It clarifies the applicability conditions of existing spectrum calculation methods for non-thermal dark matter production, emphasizing the importance of the cold spectrum component.

Findings

Existing approximations have restrictive applicability conditions.

Special care is needed for the cold component of the spectrum.

Implications for interpreting Lyman-alpha forest data.

Abstract

For the Warm Dark Matter (WDM) candidates the momentum distribution of particles becomes important, since it can be probed with observations of Lyman-$\alpha$ forest structures and confronted with coarse grained phase space density in galaxy clusters. We recall the calculation bt Kaplinghat (2005) of the spectrum in case of dark matter non-thermal production in decays of heavy particles emphasizing on the inherent applicability conditions, which are rather restrictive and sometimes ignored in literature. Cold part of the spectrum requires special care when WDM is considered.