Speaker
Description
Decaying dark matter (DDM) provides a well-motivated extension of $\Lambda$CDM, in which two-body decays -- characterized by a decay rate $\Gamma$ and velocity kick $v_k$ -- naturally suppress structure growth and lead to lower clustering amplitudes consistent with weak lensing measurements of $S_8$. Previous analyses combining Planck, BAO, and weak lensing data identified viable parameter space around $\Gamma^{-1} \sim 7\,\mathrm{Gyr}$ and $v_k \sim 1250\,\mathrm{km/s}$. Extending these constraints with upcoming cluster abundance measurements from eROSITA, however, requires accurate theoretical predictions for the halo mass function in DDM cosmologies.
We show that the standard Press-Schechter formalism, even when supplied with the correct DDM linear power spectrum, systematically overpredicts the abundance of massive halos compared to DDM $N$-body simulations. This discrepancy arises from neglecting the distinct collapse physics of DDM, primarily from mass loss as daughter particles receive velocity kicks exceeding the escape velocity. We develop a spherical collapse framework that self-consistently incorporates these effects, yielding a mass-dependent critical density threshold $\delta_c(M)$ that increases for low-mass halos unable to retain kicked daughters. We further show that this general two-body decay model admits two physically transparent limiting cases: at low masses, where all daughters escape, the collapse reduces to an effective one-body decay problem, admitting a universal fitting formula for $\delta_c$ that accurately describes one-body decay models; at high masses, where all daughters remain bound, we derive an analytic mass-independent expression for $\delta_c$. We further demonstrate that the DDM halo mass function can be accurately matched to that of warm dark matter (WDM) through an empirical mapping of DDM parameters to an effective WDM thermal mass, a correspondence long observed in $N$-body simulations but lacking a theoretical underpinning.
Together, these results extend the spherical collapse formalism to both unstable and warm dark matter cosmologies, providing the theoretical foundation needed to exploit upcoming eROSITA cluster counts for precision constraints on these models.