Improved Halo Model Calibrations for Mixed Dark Matter Models of Ultralight Axions

We study the implications of relaxing the requirement for ultralight axions to account for all dark matter in the Universe by examining mixed dark matter (MDM) cosmologies with axion fractions $f \leq 0.3$ within the fuzzy dark matter (FDM) window $10^{-25}$ eV $\lesssim m \lesssim 10^{-23}$ eV. Our simulations, using a new MDM gravity solver implemented in AxiREPO, capture wave dynamics across various scales with high accuracy down to redshifts $z\approx 1$. We identify halos with Rockstar using the CDM component and find good agreement of inferred halo mass functions (HMFs) and concentration-mass relations with theoretical models across redshifts $z=1-10$. This justifies our halo finder approach a posteriori as well as the assumptions underlying the MDM halo model AxionHMcode. Using the inferred axion halo mass - cold halo mass relation $M_{\text{a}}(M_{\text{c}})$ and calibrating a generalised smoothing parameter $\alpha$ to our MDM simulations, we present a new version of AxionHMcode. The code exhibits excellent agreement with simulations on scales $k< 20 \ h$ cMpc$^{-1}$ at redshifts $z=1-3.5$ for $f\leq 0.1$ around the fiducial axion mass $m = 10^{-24.5}$ eV $ = 3.16\times 10^{-25}$ eV, with maximum deviations remaining below 10%. For axion fractions $f\leq 0.3$, the model maintains accuracy with deviations under 20% at redshifts $z\approx 1$ and scales $k< 10 \ h$ cMpc$^{-1}$, though deviations can reach up to 30% for higher redshifts when $f=0.3$. Reducing the run-time for a single evaluation of AxionHMcode to below $1$ minute, these results highlight the potential of AxionHMcode to provide a robust framework for parameter sampling across MDM cosmologies in Bayesian constraint and forecast analyses.