2026/07/21 by Thomas Montandon, Vivian Poulin, Oliver Hahn +2
#astro-ph.CO
We present a semi-analytical framework for the halo mass function (HMF) in decaying dark matter (DDM) cosmologies, in which dark matter decays into a massive daughter particle inheriting a velocity kick vk and a massless dark radiation component. Building on the Press-Schechter formalism, we encode the DDM physics through a spherical collapse model that explicitly tracks the decay-induced mass loss, yielding a modified, mass-dependent critical collapse threshold δc(M0) and a mapping M\rm coll(M0) between the initial Lagrangian mass and the collapsed halo mass. The critical threshold exhibits a characteristic transition between two analytically tractable plateaus: a large-mass limit, where all daughter particles are retained by the halo, and a small-mass limit, where all daughters escape and the collapse is equivalent to that of a dark matter species decaying entirely into dark radiation, making δc independent of M0 and vk. We provide semi-analytical results and fits for both limits and a fitting formula for the transition, whose single free parameter M1 ∝ vk3 Γ-1/2 t\rm ta has a transparent physical interpretation: it is the mass scale at which the kick velocity equals the halo orbital velocity. We validate our predictions against a suite of N-body simulations at z=0 and z≈ 1, finding good agreement across models spanning mild to strong HMF suppression relative to ΛCDM. Residual deviations for the largest kick velocities at z=0 are observed. Via a halo-by-halo comparison between simulations, we trace the discrepancy to the definition of the halo mass when daughter orbits extend beyond the halo boundary. The resulting fitting functions for δc(M0,Γ,vk) and M\rm coll(M0) provide an efficient and accurate route to DDM constraints from current and forthcoming probes of the halo mass function.