Halo mass functions in mixed cold and fuzzy dark matter models

arXiv:2606.06599 · astro-ph.CO · Submitted 2026-06-04 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Today's paper: "Halo mass functions in mixed cold and fuzzy dark matter models".

Jocelyn: Halo mass functions in mixed cold and fuzzy dark matter models investigate how combining cold dark matter (CDM) and fuzzy dark matter (FDM) components alters structure formation,

Vera: First, who's behind it and why it matters.

Paper summary: Vera: So, to recap where we are, we've discussed how this paper investigates the halo mass functions in mixed cold and fuzzy dark matter models. Essentially, the central thesis is that combining CDM with a small fraction of fuzzy dark matter introduces a specific physical effect: FDM traces the large-scale structure like CDM does, but it simultaneously imposes smoothing on smaller scales due to wave interference effects.

Jocelyn: That means the paper claims that this mixing doesn't just change the overall density; it fundamentally alters how structures assemble, leading directly to a systematic reduction in the abundance of low-mass haloes.

Subrahmanyan: The importance lies in how this affects our standard cosmological picture; by relaxing some constraints that apply to pure FDM models and retaining CDM-like clustering on large scales, MDM provides an alternative framework where multiple dark matter species coexist and remain relatively unexplored.

Vera: It matters because it suggests a way to explore dark matter physics that retains the success of CDM on the largest scales while introducing subtle modifications at smaller scales, which is something we need to keep in mind when interpreting our data from telescopes.

Jocelyn: And the authors' development of that grid-based pipeline for identifying haloes is significant because it provides a physically consistent way to treat both species simultaneously within their numerical simulations.

Subrahmanyan: That consistency in the identification methodology is crucial because it allows them to derive meaningful results about the HMF without introducing artifacts from treating these two very different types of dark matter as separate entities during the simulation process.

Vera: So, when we look at this paper, we're seeing a detailed exploration of how a specific physical mechanism—wave interference—translates into a measurable effect on astrophysical observables like the halo mass function.

Jocelyn: And it opens up avenues for theoretical work to explore dark matter candidates beyond simple pure CDM or pure FDM scenarios by looking at these mixed compositions.

Subrahmanyan: It gives theorists a concrete tool, that suppression function R, to map the theoretical HMFs of MDM models onto the established CDM HMFs, which is a really useful connection for connecting theory to observation.

Vera: That connection is what makes this work valuable; it bridges the gap between complex numerical simulations and the observational data we gather from surveys across various redshifts.

Jocelyn: It really shows how subtle physics in dark matter can have distinct, quantifiable impacts on structure formation that we might otherwise miss if we only looked at one component at a time.

Subrahmanyan: So, the paper lays out that MDM models are a viable extension of standard CDM because they offer a way to retain large-scale stability while allowing for small-scale suppression through wave effects.

Conclusion: Vera: Wrapping up this discussion on "Halo mass functions in mixed cold and fuzzy dark matter models," we see that the authors, Johnston et al., have successfully created a framework for exploring MDM cosmologies using numerical simulations.

Jocelyn: I think it’s significant because they didn't just report a finding; they developed a unified grid-based halo finder that handles both species consistently, which makes their results more trustworthy than models that might use ad hoc methods.

Subrahmanyan: Indeed, the implication is that this paper provides a practical pathway for connecting the theoretical properties of ultralight axion-like particles to observable predictions for structure formation across different cosmic epochs.

Vera: So, in simple terms, the paper suggests that if dark matter has a small fuzzy component, we should expect to see a slightly less populated universe at smaller scales than standard CDM predicts due to the wave interference effects.

Jocelyn: That’s what it means for us observing structure: we might need to adjust our expectations for how many small haloes we count based on the underlying dark matter model we assume is correct.

Subrahmanyan: It gives cosmologists a way to test different dark matter models by looking at the HMF shape, and this paper provides a transformation tool that allows us to do that across redshift ranges from one to four.

Vera: I think the main implication is that MDM offers a flexible extension of CDM, allowing theorists to keep exploring interesting physics in dark matter without immediately discarding the successful standard model of structure formation.

Jocelyn: It means we can use these theoretical tools to inform future observational programs by predicting specific deviations from the expected HMF shape in our galaxy and beyond.

Subrahmanyan: The work establishes a solid foundation for using these MDM models as a concrete, testable alternative to pure CDM, providing a framework that connects the non-linear structure of dark matter directly to potential observations we can make with future surveys.

Sarah C. Johnston, Simon May, Tibor Dome, Sownak Bose, Alastair Basden, Carlton Baugh

Institute for Computational Cosmology, Department of Physics, Durham University · Fakultät für Physik, Universität Bielefeld · Institute of Astronomy, University of Cambridge

astro-ph.CO

Submitted: 2026-06-04

Updated: 2026-10-05

Comments: 20 pages, 13 Figures, 2 Tables, Accepted for publication in MNRAS

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 76/100

The gist: Halo mass functions in mixed cold and fuzzy dark matter models investigate how combining cold dark matter (CDM) and fuzzy dark matter (FDM) components alters structure formation, revealing that FDM

Key concepts

Mixed Dark Matter Models (MDM)
These models combine standard cold dark matter with an ultralight axion-like component (FDM). The FDM is modeled as a classical field governed by non-linear Schrödinger-Poisson equations. CDM dominates the total density, and baryons are absorbed into it.
Wave Interference Effects
The fuzzy nature of FDM causes wave interference that suppresses small-scale structure formation. This effect reduces the abundance of low-mass haloes and delays their formation compared to pure CDM scenarios.
Halo Mass Function (HMF) Suppression
Increasing the fraction of FDM systematically shifts the HMF downward and flattens its high-mass slope. This is quantified by a suppression function that maps standard CDM results to MDM results, showing a reduction in low-mass halo counts.
Grid-Based Halo Finding Pipeline
A novel method was developed to find haloes in mixed models. It combines particle-based CDM and wave-like FDM into a unified density grid using a cloud-in-cell method, allowing for consistent identification of overdensities across both components.

Terminology

Summary

Halo mass functions in mixed cold and fuzzy dark matter models investigate how combining cold dark matter (CDM) and fuzzy dark matter (FDM) components alters structure formation, revealing that FDM traces large-scale CDM while suppressing small-scale structure through wave interference, leading to a systematic downward shift in the halo mass function dependent on the FDM fraction.

The Gist

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.

Mixed Dark Matter Models and Physics

The study investigates mixed cold and fuzzy dark matter (MDM) cosmologies where an ultralight axion-like component with mass m = 10−24.5 eV constitutes a fraction f ≤ 0.3 of the total dark matter, in addition to CDM. The FDM component is modeled as a minimally coupled classical field characterized by its mass, described by the non-linear Schrödinger-Poisson equations (Equations 4 and 5). The FDM fraction is defined either cosmologically or as the ratio of FDM to total dark matter. In MDM scenarios, CDM dominates, and baryons are absorbed into the CDM component.

Halo Identification Methodology

To handle the mixed species, a grid-based halo-finding pipeline was developed within the AxiREPO framework. This method combines particle-based CDM and wave-like FDM components into a unified density field by first modifying the CDM component to be on a grid using a cloud-in-cell (CIC) method. The two components are then combined into a final Density Grid field using equations (6) and (7), resulting in an absolute value squared of the 'artificially constructed' FDM grid representing the total dark matter density. Haloes are identified by looking for overdensities on this Cartesian mesh, utilizing a modified version of the Friends-of-Friends (FOF) algorithm adapted for a discretized density mesh.

Impact on Halo Mass Function (HMF)

The simulation results show that FDM traces the CDM component on large scales, consistent with strong cross-correlation between auto and cross power spectra at low wave numbers. However, increasing the fraction of FDM inhibits the formation of small-scale structures, leading to a reduction in the abundance of low-mass haloes and a delay in their formation. This effect is quantified by observing that increasing the FDM fraction produces a systematic downward shift in the HMF and modifies its high-mass slope, resulting in a progressive suppression and flattening of the HMF.

Phenomenological Mapping

A phenomenological model was introduced to map CDM HMFs to their MDM counterparts using a suppression function with parameters dependent on redshift and FDM fraction. This model is formulated as:

R = 1 + (M S / M) (-α - β), where M S is the suppression mass scale, and α and β are linear functions of the FDM fraction (f) and redshift (z). This function reproduces simulated HMFs within approximately 0.1 to 0.2 dex across the parameter space explored (1 ≤ z ≤ 4, f ≤ 0.3).

Conclusion

The study concludes that MDM models provide a flexible and viable extension to the standard CDM paradigm, with distinct but subtle signatures in the nonlinear structure of the Universe. The developed grid-based halo finder provides a unified and physically consistent treatment of both species, establishing a framework for exploring MDM cosmologies without requiring dedicated simulations for each parameter choice.

Future Work

Future work could explore a wider range of axion masses, improve simulation resolution, extend the HMF transformation model to include additional parameters like axion mass or environmental dependence, and incorporate baryonic physics to better assess degeneracies with observational data. The authors suggest that fitting for fractions f > 0.3 would not be beneficial due to observational constraints.

Key Findings Summary:

  1. FDM traces the CDM distribution on large scales, as evidenced by a strong cross-correlation coefficient r(k) at low k values.

  2. Wave interference effects in FDM suppress small-scale power, leading to a reduction in the abundance of low-mass haloes.

  3. Increasing FDM fraction produces a systematic downward shift in the HMF and modifies its high-mass slope.

  4. A phenomenological transformation model successfully maps CDM HMFs to MDM counterparts, reproducing simulated results within 0.1 to 0.2 dex for the explored parameter space (1 ≤ z ≤ 4, f ≤ 0.3).

  5. The grid-based halo finder provides a unified and physically consistent treatment by treating both species self-consistently as an overdensity in the total dark matter field.

Improvements for AI systems

Here are specific improvements to AI systems derived from the methodologies and findings presented in this paper:

  1. Automated Halo Mass Function (HMF) Inversion for Dark Matter Models:

  2. Cross-species structure formation prediction using a unified density field approach:

  3. Phenomenological HMF transformation modeling for parameter estimation in mixed dark matter cosmologies:

  4. Robust halo identification pipelines for multi-species simulations (CDM + FDM):

  1. Automated Halo Mass Function (HMF) Inversion for Dark Matter Models:

This system can take a set of observed or simulated HMFs from different cosmic models and use the derived fitting formula (Equation 11, e.g., in Section 4.2) to rapidly infer the underlying cosmological parameters, specifically the FDM fraction and redshift evolution, without running full N-body simulations for every parameter combination. It can predict the expected HMF shape for a given set of input parameters with a stated accuracy (e.g., ±0.1 dex).

  1. Cross-species Structure Formation Prediction using a Unified Density Field Approach:

The AI can utilize the AxiREPO framework's grid-based halo finding pipeline (Section 2.3) to process combined density fields from both CDM particle distributions and FDM wavefields simultaneously. This allows the system to identify haloes consistently across different species, overcoming the limitations of single-species approximations used in prior methods (Section 2.3.4). The improved AI can then track how structure formation (filamentary morphology, void prominence) changes as the FDM fraction increases, providing a direct comparison between CDM and MDM structure evolution at specific redshifts.

  1. Phenomenological HMF Transformation Modeling for Parameter Estimation in Mixed Dark Matter Cosmologies:

The system can implement the non-linear least squares fitting procedure (Equation 12, Section 4.3) to map observed MDM HMFs onto a parameterized transformation function (Equation 11). This allows the AI to determine the characteristic suppression mass scale parameters—such as the linear scaling parameters for redshift and FDM fraction—by minimizing the misfit between simulated/observed data and the model prediction. This enables a dark matter parameter inference capability, where observational constraints on HMFs are used to constrain fundamental cosmological properties like axion mass or dark matter fractions.

  1. Robust Halo Identification Pipelines for Multi-species Simulations (CDM + FDM):

The system can be designed as a self-consistent halo finder that treats the total dark matter density field as a single entity by combining particle and grid components (Equation 6, Section 2.3.1). This joint grid-based finding method ensures that the resulting halo catalogue is physically consistent across both species. The AI can then be used to compare the results of this unified finder against traditional methods (like FOF) and single-species proxies, quantifying the systematic bias introduced by different identification schemes in mixed-species environments.

Sources

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