Halo mass functions in mixed cold and fuzzy dark matter models

We investigate the impact of mixed cold and fuzzy dark matter (MDM) cosmologies on the halo mass function (HMF) using numerical simulations performed with the AxiREPO framework. We consider models in which an ultralight axion-like component with mass $m =10^{-24.5} \mathrm{eV}$ constitutes a fraction $f \leq 0.3$ of the total dark matter. To enable consistent halo identification in mixed-species scenarios, we develop a grid-based halo-finding pipeline that combines the particle-based cold dark matter (CDM) and wave-like fuzzy dark matter (FDM) components into a unified density field. We find that FDM traces the large-scale CDM distribution while suppressing small-scale structure through wave interference effects, leading to a reduction in the abundance of low-mass haloes and modifying the HMF in a manner dependent on redshift and FDM fraction. Increasing the FDM fraction produces a systematic downward shift in the HMF and modifies its high-mass slope. Motivated by these trends, we introduce a phenomenological model that maps CDM HMFs to their MDM counterparts using a suppression function with parameters dependent on redshift and FDM fraction. This model reproduces the simulated HMFs within approximately 0.1 to 0.2 dex across the parameter space explored ($1 \leq z \leq 4$, $f \leq 0.3$). Our results provide a computationally efficient method for predicting structure formation in MDM cosmologies without requiring dedicated simulations for each parameter choice, and establish a framework for exploring the impact of MDM on cosmological structure formation.