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arxiv: 2606.30739 · v1 · pith:CWPMNAX3new · submitted 2026-06-29 · 🌌 astro-ph.CO · astro-ph.GA

Fuzzy Dark Matter Halo Mass Functions at Cosmic Dawn

Raghunath Ghara , Adam Lidz , Daniel Grin , Jackson Sipple This is my paper

Pith reviewed 2026-07-01 01:54 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.GA
keywords fuzzy dark matterhalo mass functioncosmic dawnN-body simulationsmixed dark matterJWSTultraviolet luminosity function
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The pith

A new fitting formula for fuzzy dark matter halo mass functions at redshifts 6-11 shows weaker suppression than previous simulation results.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper runs N-body simulations of fuzzy dark matter and mixed models to derive a calibrated halo mass function. It removes spurious halos from numerical noise and provides a fitting formula valid for z=6-11. This matters for predicting the abundance of small halos that seed early galaxies, which JWST can observe through the ultraviolet luminosity function. The new formula indicates about 30 percent less suppression at certain masses compared to earlier fits.

Core claim

We provide a new halo mass function fitting formula, calibrated over z=6-11, applicable to pure FDM and mixed dark matter scenarios. For m c² = 10^{-21} eV and M ∼ 3 × 10^9 M_⊙ we find a ∼30% weaker suppression than earlier simulation-based formulas predict, which we attribute to their extrapolation beyond the m_FDM range previously simulated.

What carries the argument

The new halo mass function fitting formula, obtained from N-body simulations after identifying and removing spurious halos due to discreteness noise.

If this is right

  • The fitting formula applies to both pure fuzzy dark matter and mixed fuzzy-cold dark matter models.
  • It shows better agreement with prior simulation-based formulas than with semi-analytic models.
  • Upcoming JWST observations of the UVLF probing M_UV ≳ -13 at z ≳ 10 will test these models.
  • The formula can be used to model delayed galaxy formation during cosmic dawn in fuzzy dark matter cosmologies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Extending the simulations to lower FDM masses or higher redshifts could further refine the formula.
  • The weaker suppression might allow more early galaxies than previously modeled, affecting reionization timelines.
  • Direct comparison with upcoming lensed galaxy counts could confirm or refute the 30% difference.

Load-bearing premise

The procedure for identifying and removing spurious halos accurately quantifies and corrects the systematic uncertainty without removing genuine halos.

What would settle it

Running higher-resolution simulations or comparing the predicted halo number densities directly against observed galaxy counts at z greater than 10 for halo masses around 3 times 10^9 solar masses.

Figures

Figures reproduced from arXiv: 2606.30739 by Adam Lidz, Daniel Grin, Jackson Sipple, Raghunath Ghara.

Figure 1
Figure 1. Figure 1: Comparison of different HMFs in an FDM model with m22 = 10 at z = 8. The top panel shows the FDM HMFs computed using different prescriptions, along with the corresponding CDM HMF. The bottom panel displays the ratio of the CDM to FDM HMFs as a function of halo mass. See Appendix A for detailed descriptions of each model. imately account for modified linear growth in FDM [FDM￾TH-δc(M)] (e.g. Marsh & Silk 20… view at source ↗
Figure 2
Figure 2. Figure 2: Dimensionless power spectra ∆2 (k) = k 3P(k)/2π 2 at z = 100 for the different dark matter scenarios considered in this study. The suppression in the initial power spectrum from FDM moves to smaller scales (higher k) with increasing m22, while the fluctuations are less strongly suppressed as the FDM fraction fF decreases. The initial conditions for our N-body simulations follow these power spectrum models.… view at source ↗
Figure 3
Figure 3. Figure 3: The proto-halo sphericity (top) and overlap (bottom) coefficients as a function of halo mass at z = 8. The black points and error bars show the CDM results, while the green ones show the same for an FDM model with m22 = 1 and fF = 1. The shaded regions show the 2σ spread. Note that the simulated halo abundance is small at M ≳ 1010.5M⊙, leading to noise in the shaded boundaries. Low mass FDM halos often sho… view at source ↗
Figure 4
Figure 4. Figure 4: The top panel shows the z = 8 CDM and FDM HMFs for m22 = 1. The black stars show the CDM HMF after remov￾ing dark matter halos with S and O coefficients smaller than ST and OT, respectively. The grey squares are the (nearly identical) CDM results without excising halos. The green squares give the FDM HMF without removing halos, while the green circles show the FDM HMF (mean and 1σ Poisson error bars) after… view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: The ratio of CDM and FDM HMFs at z = 8 for the full range of FDM scenarios considered in this work. The solid curves establish that our new fitting formula successfully describes this full range of models. – for the most lenient cut shown in the figure with ST and OT both = 0.1, compared to the most stringent case with ST and OT = 0.4. However, the sensitivity to threshold choice is confined to high R port… view at source ↗
Figure 7
Figure 7. Figure 7: Ratio of the CDM and FDM HMFs (R) as a function of halo mass for different combinations of ST and OT in pure FDM models with m22 = 1 (top), m22 = 10 (middle), and m22 = 20 (bottom) at a representative redshift of z = 8. The solid blue lines show our fitting formula, while the dashed blue are from S2016. intermediate m22 mixed DM scenarios, in order to cover the transition between the two fitting formulas. … view at source ↗
Figure 9
Figure 9. Figure 9: UVLF models and current data for m22 = 5 and fF = 1 at z = 8, 10 and 12. The black curve assumes the CDM HMF, while other curves are for different FDM HMF/UVLF models. The points with 1σ error bars show UVLF measurements from Bouwens et al. (2021) (blue, field galaxies) and Bouwens et al. (2022) (red, lensed galaxies). Our new HMF model should be used to refine previous FDM constraints from the UVLFs and t… view at source ↗
Figure 10
Figure 10. Figure 10: UVLF models and data at z = 8 − 12 for mixed FDM-CDM scenarios. The curves show example scenarios with different m22 and fF values, computed using the fitting formula of Equation 4 and the conditional luminosity function from Equation 5. The data points are the same as in [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The cumulative abundance of dark matter halos for m22 = 5 and fF = 1 at z = 8, 10 and 12. The black curve is for CDM, while the other curves show different HMF model variants for FDM. 108 109 1010 Mmin(M ) 10−2 10−1 100 101 N(> Mmin, z) z = 8 108 109 1010 Mmin(M ) 10−2 100 z = 10 108 109 1010 Mmin(M ) 10−4 10−3 10−2 10−1 100 z = 12 CDM m22 = 1, fF = 1 m22 = 5, fF = 1 m22 = 5, fF = 0.3 m22 = 5, fF = 0.5 [… view at source ↗
Figure 12
Figure 12. Figure 12: The cumulative abundance of dark matter halos at z = 8, 10 and 12 for the different dark matter scenarios considered in this study. Here, we use the fitting formula of Equation 4. while the FDM-Schive HMF yields the maximum ratio. This spread follows the trends seen for the HMFs in Section 2. In this case (z = 8, m22 = 5, MAB = −12), our new fitting formula anchors the CDM to FDM UVLF ratio at 7.1, clos￾e… view at source ↗
read the original abstract

In fuzzy dark matter (FDM) cosmological models, wave effects impact astrophysical length scales, suppressing the abundance of small mass dark matter halos, and delaying the earliest phases of galaxy formation during Cosmic Dawn. Current and upcoming James Webb Space Telescope (JWST) measurements of the galaxy ultraviolet luminosity function (UVLF) will allow unprecedented tests of this suppression, yet significant uncertainties remain in theoretical models of the FDM halo mass function. We run a new suite of N-body simulations with FDM particle masses of $mc^{2}=10^{-22}\,{\rm eV} - 2 \times 10^{-21}$ eV and mixed FDM-cold dark matter (CDM) models with FDM mass fractions of $f_{\mathrm{F}} = 0.3-1$. We identify and remove spurious halos from discreteness noise and quantify the associated systematic uncertainty. We provide a new halo mass function fitting formula, calibrated over $z=6-11$, applicable to pure FDM and mixed dark matter scenarios. Our results are in better agreement with previous simulation-based fitting formulas than with current semi-analytic mass function models. Nevertheless, for $m c^{2} = 10^{-21}$ eV and $M \sim 3 \times 10^9 M_\odot$ we find a $\sim 30\%$ weaker suppression than earlier simulation-based formulas predict, which we attribute to their extrapolation beyond the $m_{\rm FDM}$ range previously simulated. Applying our fitting formula to the UVLF, we find that upcoming JWST observations behind foreground lensing clusters, probing $M_{\rm UV} \gtrsim -13$ at $z \gtrsim 10$, will provide a powerful test of FDM and mixed dark matter models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript runs new N-body simulations of pure FDM (mc² = 10^{-22}–2×10^{-21} eV) and mixed FDM-CDM models (f_F = 0.3–1), removes spurious halos from discreteness noise while quantifying the associated systematic uncertainty, and calibrates a new halo mass function fitting formula over z = 6–11. The formula is stated to apply to both pure and mixed scenarios; the authors report ~30% weaker suppression than earlier simulation-based formulas at mc² = 10^{-21} eV and M ∼ 3×10^9 M_⊙ (attributed to prior extrapolation), find better agreement with previous simulation-based fits than with semi-analytic models, and discuss implications for JWST UVLF constraints.

Significance. If the spurious-halo removal is shown to be robust, the work supplies a directly calibrated fitting formula for high-redshift FDM halo abundances that improves upon semi-analytic prescriptions and yields concrete, falsifiable predictions for lensed JWST UVLF measurements at M_UV ≳ −13 and z ≳ 10. The explicit quantification of cleaning systematics and the extension to mixed models are positive features.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (halo identification): The headline numerical result—a ~30% weaker suppression at mc² = 10^{-21} eV, M ∼ 3×10^9 M_⊙—rests entirely on the post-cleaning catalog. No explicit criteria for flagging spurious halos, no resolution-convergence tests at the relevant mass and redshift, and no demonstration that genuine FDM halos remain untouched are provided; without these, it is impossible to assess whether the reported difference from earlier formulas is physical or an artifact of the removal step.
  2. [§4] §4 (comparison and fitting formula): The new fitting formula is calibrated directly to the cleaned simulations, yet the manuscript does not show the raw versus cleaned mass functions, the effect of varying the cleaning threshold on the 30% discrepancy, or how the quoted systematic uncertainty brackets residual contamination at the quoted mass and redshift.
minor comments (1)
  1. [Abstract] Abstract: the FDM mass range is written as 10^{-22} eV – 2×10^{-21} eV; confirm whether the bounds are inclusive and whether the mixed-model runs use the same particle masses.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation of our methods and results.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (halo identification): The headline numerical result—a ~30% weaker suppression at mc² = 10^{-21} eV, M ∼ 3×10^9 M_⊙—rests entirely on the post-cleaning catalog. No explicit criteria for flagging spurious halos, no resolution-convergence tests at the relevant mass and redshift, and no demonstration that genuine FDM halos remain untouched are provided; without these, it is impossible to assess whether the reported difference from earlier formulas is physical or an artifact of the removal step.

    Authors: We appreciate the referee highlighting the need for greater clarity on the halo-cleaning procedure. While §3 describes the removal of spurious halos due to discreteness noise and quantifies the associated systematic uncertainty, we agree that explicit flagging criteria, resolution-convergence tests at the relevant masses and redshifts, and explicit validation that genuine FDM halos are unaffected should be presented more directly. In the revised manuscript we will add these elements to demonstrate that the ~30% weaker suppression is physical rather than an artifact. revision: yes

  2. Referee: [§4] §4 (comparison and fitting formula): The new fitting formula is calibrated directly to the cleaned simulations, yet the manuscript does not show the raw versus cleaned mass functions, the effect of varying the cleaning threshold on the 30% discrepancy, or how the quoted systematic uncertainty brackets residual contamination at the quoted mass and redshift.

    Authors: We agree that direct comparisons would help readers evaluate the cleaning step. In the revised version we will include raw versus cleaned mass-function comparisons, examine the sensitivity of the reported 30% discrepancy to changes in the cleaning threshold, and clarify how the quoted systematic uncertainty encompasses possible residual contamination at the masses and redshifts of interest. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained calibration to new simulations

full rationale

The paper runs new N-body simulations for specified FDM masses and mixed models, removes spurious halos while quantifying systematic uncertainty, and calibrates a new fitting formula directly to those results over z=6-11. This is an explicit empirical calibration rather than any reduction by construction, self-definition, or load-bearing self-citation. The reported 30% difference is presented as a comparison to prior work (attributed to extrapolation range), with no equations or steps shown that equate outputs to inputs by definition. The derivation chain remains independent of the target result.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim depends on the accuracy of N-body evolution for FDM wave effects, the completeness of spurious-halo identification, and the assumption that the chosen mass and redshift range is representative for the fitting formula. No new particles or forces are postulated.

free parameters (1)
  • fitting coefficients in the new halo mass function formula
    The formula is calibrated to the simulation outputs; the coefficients are determined by fitting rather than derived from first principles.
axioms (2)
  • domain assumption N-body simulations with the chosen particle mass and force resolution correctly capture the suppression of small-scale structure due to FDM wave effects
    Invoked when running the suite and when claiming the results apply to real cosmology.
  • domain assumption The method used to identify and remove spurious halos removes only discreteness artifacts and leaves the true halo abundance unchanged within the quoted systematic uncertainty
    Central to the claim that the new formula is reliable; location is the sentence describing removal and uncertainty quantification.

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discussion (0)

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Reference graph

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