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arxiv: 2606.19104 · v1 · pith:NYFX6Y64new · submitted 2026-06-17 · 🌌 astro-ph.CO · astro-ph.IM

PHANTOM: A MATLAB and Octave Toolbox Connecting Linear Field Statistics to Dark Matter Halo Observables

Mohammad Abu Thaher Chowdhury This is my paper

Pith reviewed 2026-06-26 19:43 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IM
keywords dark matter haloslinear power spectrumhalo mass functionMATLAB toolboxcosmology calculationsdensity profilesfuzzy dark mattercorrelation function
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The pith

PHANTOM supplies MATLAB and Octave users with a validated set of routines that link linear density field statistics directly to dark matter halo observables through a reusable cosmology structure.

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

The paper presents PHANTOM, a toolbox that fills the absence of native implementations for these calculations in MATLAB and Octave. It organizes computations around a cosmology structure that holds expansion history, growth factors, and power spectrum information. This structure is passed to all modules so that halo mass functions, bias, profiles, and observables stay consistent with the linear field inputs. Validation against Python packages shows sub-percent agreement on common quantities. The result is a single entry point for obtaining power spectra, variances, correlation functions, mass functions, and density profiles on user grids for cold, warm, and fuzzy dark matter.

Core claim

PHANTOM provides a single-entry-point interface where a cosmology structure carries background expansion, growth factors, and linear power spectrum handles, allowing users to compute field statistics, halo statistics, and halo observables on arbitrary grids while maintaining internal consistency for cold, warm, and fuzzy dark matter models.

What carries the argument

The cosmology structure that stores background expansion, growth, and linear power-spectrum handles and is passed through the call graph to enforce consistency.

If this is right

  • Halo statistics and structure calculations remain consistent by design when the input cosmology is updated.
  • Users obtain field statistics, halo statistics, and halo observables on arbitrary user-defined grids from one entry point.
  • The same interface supports cold, warm, and fuzzy dark matter scenarios without separate code paths.
  • Enclosed mass, circular velocity, projected density, and lensing convergence become available directly alongside the linear field quantities.

Where Pith is reading between the lines

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

  • MATLAB-based analysis pipelines can incorporate these calculations without switching languages or relying on external calls.
  • The single-structure design could reduce bookkeeping errors during systematic variation of cosmological parameters.
  • New observables could be added by writing functions that accept the existing cosmology structure, preserving consistency automatically.

Load-bearing premise

Sub-percent agreement with existing Python implementations on selected quantities is sufficient to confirm correctness of the MATLAB and Octave implementations across all user-defined grids and dark matter scenarios.

What would settle it

A statistically significant mismatch on a grid or dark matter model outside the validated set when compared to independent analytic expectations or higher-precision simulations.

Figures

Figures reproduced from arXiv: 2606.19104 by Mohammad Abu Thaher Chowdhury.

Figure 1
Figure 1. Figure 1: — phantom software architecture. The cosmology struct (shaded boxes) is constructed once and propagated as a function-handle container throughout the package. Arrows indicate data flow: the linear power spectrum feeds the variance calculation, which in turn drives the halo mass function and bias modules. The concentration–mass relation takes the halo mass and cosmology as inputs and, together with the viri… view at source ↗
Figure 3
Figure 3. Figure 3: WDM produces a smooth exponential cutoff that [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: — Comparison of the matter variance σ(R) between phan￾tom (solid black) and hmf (Murray et al. 2013) (blue dashed) for the EH98 zero-baryon transfer function at z = 0. The lower sub￾panel shows the ratio σphantom/σhmf; the two codes agree within 2% across the plotted mass range. or axionCAMB) propagates automatically into the cor￾relation function without additional modification. Two numerical methods are … view at source ↗
Figure 3
Figure 3. Figure 3: — Linear power spectrum, variance, and correlation function from phantom for the Planck15 cosmology at z = 0, compared against colossus (Diemer 2018), and illustration of additional dark matter models and numerical options. Top row: (3a) linear matter power spectrum P(k) for the zero-baryon (EH-zb, red) and full-baryon (EH-full, blue) Eisenstein & Hu transfer functions; solid lines are colossus and dashed … view at source ↗
Figure 4
Figure 4. Figure 4: — Halo mass functions at z = 0 computed with the models implemented in phantom. Panel (4a) shows CDM predictions from several multiplicity functions; the lower sub-panel plots the ratio of each curve to colossus evaluated with the same cosmology and mass definition, demonstrating sub-percent agreement over 108 ≲ M/(h−1M⊙) ≲ 1014. Panel (4b) compares the phantom CDM halo mass function against hmf (Murray et… view at source ↗
Figure 5
Figure 5. Figure 5: — CDM density profiles computed by phantom (solid lines) compared to colossus (Diemer 2018) (dashed lines) for a halo of M200c = 1014 M⊙ h−1 , c = 5, z = 0. The lower panel shows the ratio ρPHANTOM/ρCol. NFW and Hernquist agree at the 0.1 per cent level across the full radial range. The Einasto profile shows a constant ∼0.5 per cent offset arising from the peak-height mass￾definition convention (Section 5.… view at source ↗
Figure 6
Figure 6. Figure 6: — Composite FDM density profiles computed by phan￾tom at z = 0 for three halo masses: Mvir ∈ {1010 , 1012 , 1014} M⊙ (magenta, blue, and red, respectively). For the analytic profiles (blue, red), solid lines show the full composite ρ(r); dashed lines show the soliton component ρsol; dotted lines show the NFW outer halo ρNFW. For the dwarf-scale case (Mvir = 1010 M⊙, magenta), cross markers show the radiall… view at source ↗
Figure 7
Figure 7. Figure 7: — Concentration–mass relations at z = 0 from phantom. Panel (a): Five representative CDM models compared against colossus (Diemer 2018). Solid lines show phantom outputs; dashed lines of matching colour show the corresponding colossus predictions for bullock01 (Bullock et al. 2001), dutton14 (Dutton & Macci`o 2014), klypin16 (Klypin et al. 2016), ludlow16 (Ludlow et al. 2016), and ishiyama21 (Ishiyama et a… view at source ↗
Figure 8
Figure 8. Figure 8: — Gravitational lensing convergence κ(R) = Σ(R)/Σcr computed with phantom for a halo of M200c = 1014 h−1 M⊙, c = 5, zl = 0.3, zs = 1.0, and Planck18 cosmology. The surface mass density Σ(R) is obtained from Eq. (24) via profile observable function; Σcr follows from Eq. (46). Left: CDM profile comparison. The upper sub-panel shows κ(R) for the NFW (blue solid; Navarro et al. 1997), Hernquist (red dashed; He… view at source ↗
Figure 9
Figure 9. Figure 9: — Circular-velocity curves computed with phantom compared to SPARC rotation-curve data (Lelli et al. 2016). Left: NGC 2403, a late-type spiral with halo mass M200 = 9.4 × 1011 M⊙. Right: UGCA 442, a late-type dwarf with halo mass M200 = 6 × 1010 M⊙. In each panel the blue line shows a pure NFW profile, and the red line shows the soliton+NFW composite for FDM with boson mass m22 = 0.1 (left) and m22 = 0.3 (… view at source ↗
Figure 10
Figure 10. Figure 10: — Linear halo bias b(M, z) computed with phantom using the unified halo-bias interface. Left: b(M) at z = 0 for a Planck18 cosmology, comparing the Press–Schechter/Cole–Kaiser (blue solid; Cole & Kaiser 1989), Sheth & Tormen (orange dashed; Sheth & Tormen 1999), Sheth–Mo–Tormen moving-barrier (green dash-dotted; Sheth et al. 2001), and Tinker et al. (red dotted; Tinker et al. 2010) prescriptions. Right: R… view at source ↗
read the original abstract

We present phantom (Profile and Halo Analysis for Numerous Theoretical dark Matter Observables), a public MATLAB toolbox and Octave package for calculations that connect the linear density field to dark matter halo observables. The package combines a flexible cosmology module with linear power spectrum, variance, and correlation function solvers, and a halo module that covers mass functions, linear bias, density profiles, and concentration-mass relations for cold, warm, and fuzzy dark matter scenarios. All core routines are validated against the Python package colossus, hmf, and halomod, yielding sub-percent agreement for shared models across distances, power spectra, variance, correlation functions, halo mass functions, and density profiles. Phantom is organised around a cosmology structure that stores background expansion, growth, and linear power-spectrum handles; this object is constructed once and passed through the call graph, so that halo statistics and halo structure calculations remain consistent by design. From this single entry point, users can obtain field statistics (power spectrum, variance, correlation function), halo statistics (mass functions, linear bias), and halo observables (enclosed mass, circular velocity, projected density, and lensing convergence) on arbitrary user-defined grids. The toolbox targets users whose analysis pipelines are written in MATLAB or Octave, where a validated native implementation of these models has been absent. The code is released under the MIT licence at phantom(https://github.com/matc-thaher/PHANTOM).

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

1 major / 1 minor

Summary. The manuscript presents PHANTOM, a public MATLAB and Octave toolbox for connecting linear density field statistics (power spectra, variance, correlation functions) to dark matter halo observables (mass functions, linear bias, density profiles, concentration-mass relations) for cold, warm, and fuzzy dark matter. The package is built around a single cosmology structure that stores background, growth, and power-spectrum handles and is passed through the call graph to ensure consistency. All core routines are stated to have been validated against colossus, hmf, and halomod, yielding sub-percent agreement on shared models; the code is released under the MIT licence.

Significance. If the implementations hold, the toolbox fills a documented gap by supplying validated native routines for MATLAB/Octave users who require consistent linear-to-halo calculations on arbitrary grids. The single-entry-point cosmology object is a clear design strength that enforces internal consistency across field statistics and halo modules. The reported sub-percent agreement with three independent Python packages on shared CDM quantities provides concrete evidence of correctness for those cases.

major comments (1)
  1. [Abstract] Abstract: the validation statement is explicitly limited to 'shared models' against colossus, hmf, and halomod. These packages do not implement the WDM transfer-function cut-off or FDM Jeans-scale suppression used in PHANTOM; therefore the halo-mass-function, bias, and concentration modules for WDM and FDM rest only on the authors' internal implementation and lack the same external sub-percent benchmark. This directly affects the central claim that the toolbox supplies correct implementations across all three dark-matter scenarios.
minor comments (1)
  1. [Abstract] The GitHub link in the abstract is written as 'phantom(https://github.com/matc-thaher/PHANTOM)', which appears to be a formatting or typesetting error.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the toolbox design and the careful identification of the validation scope. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the validation statement is explicitly limited to 'shared models' against colossus, hmf, and halomod. These packages do not implement the WDM transfer-function cut-off or FDM Jeans-scale suppression used in PHANTOM; therefore the halo-mass-function, bias, and concentration modules for WDM and FDM rest only on the authors' internal implementation and lack the same external sub-percent benchmark. This directly affects the central claim that the toolbox supplies correct implementations across all three dark-matter scenarios.

    Authors: We agree that the external sub-percent benchmarks are restricted to CDM quantities present in colossus, hmf, and halomod. The manuscript already qualifies the validation statement with the phrase 'for shared models', which correctly signals this limitation. For WDM and FDM the modules implement standard transfer-function cut-offs and Jeans-scale suppressions drawn from the literature (with explicit references provided in the paper and code). Internal consistency across all three scenarios is enforced by the single cosmology object. To improve clarity we will revise the abstract to state explicitly that external validation applies only to CDM shared models and will add a short paragraph in the validation section describing the literature-based implementation and consistency checks used for WDM/FDM. This revision addresses the referee's concern without altering the reported results. revision: yes

Circularity Check

0 steps flagged

No circularity; toolbox implements standard models with external validation

full rationale

The paper presents a computational toolbox for standard linear-field-to-halo calculations in CDM, WDM and FDM scenarios. Core routines are validated against independent external packages (colossus, hmf, halomod) for all shared models, with sub-percent agreement reported on power spectra, variance, mass functions and profiles. The cosmology structure is passed consistently through the call graph, but this is an implementation detail, not a self-definitional reduction. No self-citations are invoked as load-bearing premises, no fitted parameters are relabeled as predictions, and no uniqueness theorems or ansatzes are smuggled in. The derivation chain consists of established cosmological relations implemented in MATLAB/Octave; external benchmarks make the presentation self-contained against independent codes.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Relies on standard linear perturbation theory and halo model assumptions already present in the cited Python packages; no new free parameters or entities introduced.

axioms (1)
  • domain assumption Standard cosmological background expansion, linear growth, and power spectrum calculations.
    Core of the cosmology module that feeds all halo calculations.

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