A minimal Dark Matter Fissure phenomenological law reproducing SPARC rotation curves

The result and the engine are now available on : https://dmf-sparc.com/

This repository accompanies a results-first study of a minimal Dark-Matter-from-Fissures (DMF) model, in which the apparent dark matter of disk galaxies is not made of particles but arises from geometric fissures in a space–time medium under tension.

In this framework, dark matter is interpreted as a network of space–time fissures that:

• enhances the effective gravitational field at galactic scales,

• closes or locks under very high tension (reducing its effect),

• and evolves more slowly than ordinary matter, because fissures are anchored in the fabric and do not move as fast as baryons.

From this picture, the repository implements a minimal phenomenological law with:

• a scalar tension proxy built from baryonic acceleration, surface brightness and gravitational shear,

• a susceptibility function χ(T)\chi(\mathcal{T})χ(T) describing how the fissure network responds to tension (background + peak + high-tension lock),

• a simple global radial halo profile,

• a baryonic extinction depending only on the local baryon fraction,

• mild radial smoothing, representing the slower response of fissures compared to the motion of baryons,

• and one single gain parameter per galaxy (KgK_gKg), plus a global gain KDMF,globalK_{\rm DMF,global}KDMF,global.

All other parameters are fixed globally for the entire SPARC sample (no family-by-family tuning, no hand-picked cases).

Using standard SPARC-like inputs (radii, observed velocities, baryonic contributions and surface brightness profiles), the model predicts the dark–matter fraction fDM,model(R)f_{\rm DM,model}(R)fDM,model(R) and is directly compared to the required fraction fDM,req(R)f_{\rm DM,req}(R)fDM,req(R) inferred from the data.

The key point of this repository is the strength and robustness of the quantitative agreement:

• On the full SPARC-class sample, the model reproduces the disk-averaged dark–matter fraction with a mean absolute error of about 6% and a global bias below 5% (model minus data).

• The correlation between disk-averaged required and model fractions reaches r ≈ [0.99].

• By radial zone (centre, mid-disk, outer disk), the mean absolute errors are typically in the range 10%, with small systematic offsets:

  • central regions very slightly DM-poor on average (by a few percentage points),

  • outer regions mildly DM-rich (again at the level of a few percentage points),

  • mid-disk regions essentially unbiased on the sample as a whole.

These results are obtained with no per–galaxy shape tuning and a deliberately simple mapping from baryons to fissure field to dark–matter fraction. The model is therefore highly constrained and yet remains quantitatively accurate on a large and diverse galaxy sample, which is the central message of this work.

Contents of this repository

• The main paper (PDF):
  – Description of the minimal DMF framework,
  – Full mathematical specification of the phenomenological law,
  – Global statistics and discussion of results.

• Configuration files (e.g. config_simple.*):
  – All global parameters used in the minimal DMF model (tension weights, susceptibility parameters, radial profile, extinction thresholds, global gain).

• Code implementing the engine (e.g. PHP scripts):
  – Per-galaxy pipeline (tension proxy, susceptibility, halo profile, smoothing, extinction, calibration of KgK_gKg, final fDM,model(R)f_{\rm DM,model}(R)fDM,model(R)),
  – Batch runner for the full SPARC sample,
  – Curve/diagnostic exporters.

• Per-galaxy CSV files:
  – Input: (R,Vobs,Vgas,Vdisk,Vbul,SBdisk,SBbul)(R, V_{\rm obs}, V_{\rm gas}, V_{\rm disk}, V_{\rm bul}, SB_{\rm disk}, SB_{\rm bul})(R,Vobs,Vgas,Vdisk,Vbul,SBdisk,SBbul),
  – Derived quantities: gobsg_{\rm obs}gobs, gbarg_{\rm bar}gbar, fDM,req(R)f_{\rm DM,req}(R)fDM,req(R),
  – Model outputs: T(R)\mathcal{T}(R)T(R), χ(T(R))\chi(\mathcal{T}(R))χ(T(R)), F(rn)F(r_n)F(rn), E(R)E(R)E(R), S(R)S(R)S(R), fDM,model(R)f_{\rm DM,model}(R)fDM,model(R).

• Figures / plots (appendix material):
  – Example rotation curves and dark–matter fractions for representative galaxies (HSB, LSB, massive spirals, dwarfs),
  – Scatter plots of disk-averaged fDM,reqf_{\rm DM,req}fDM,req vs. fDM,modelf_{\rm DM,model}fDM,model,
  – Histograms and distributions of residuals (bias and MAE) per radial zone.

Reproducibility

The repository is designed to be fully reproducible:

• All equations are given explicitly in the paper and mirrored in the code.

• All global parameters used to produce the figures are included in the configuration files.

• The per-galaxy CSV outputs allow independent verification of each step (from baryons to fissure field to final dark–matter fraction).

• The model structure is language-agnostic: although the reference implementation is in PHP, the algorithm can be re-implemented in Python, C/C++, Julia, etc., using only this repository.

Researchers can therefore:

1. Reproduce the SPARC fits exactly,

2. Explore parameter variations around the minimal configuration,

3. Test the same DMF law on other galaxy samples.

Keywords
dark matter; galaxy rotation curves; SPARC; alternative gravity; space–time medium; fissures; phenomenological model; DMF; astrophysics