Superfluid Vacuum Theory: Galaxy Rotation Curves

A unified framework explaining galaxy rotation curves and supermassive black holes as emergent phenomena from quantum vacuum dynamics — without dark matter particles.

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📄 Paper

This repository accompanies the research paper:

Galaxy Rotation Curves from Superfluid Vacuum Theory: A Unified Framework Integrating the Vortex–Black Hole Correspondence
Shah, C. (2026)
🔗 DOI: 10.5281/zenodo.18150850

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🌌 Overview

This repository implements a theoretical framework that provides a dark matter-free explanation for galaxy rotation curves based on Superfluid Vacuum Theory (SVT). The framework makes a radical proposal:

Supermassive black holes are macroscopic topological defects (vortex cores) in the quantum vacuum, and what we call "dark matter halos" are the gravitating rotational energy of extended vortex fields anchored by these central defects.

In other words: the central black hole and the dark matter halo are two aspects of a single topological structure.

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🔬 The Physics

Core Idea

The physical vacuum is modeled as a Bose-Einstein condensate governed by the logarithmic nonlinear Schrödinger equation (Log-NLSE):

$$i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m}\nabla^2\psi + m\Phi\psi - b\ln\left(\frac{|\psi|^2}{\rho_0}\right)\psi$$

This equation has a crucial property: the speed of sound is density-independent ($c_s = \sqrt{b/m}$), providing a natural explanation for the constancy of the speed of light.

The SVT Velocity Formula

The vacuum contribution to galaxy rotation curves is:

$$V_{\text{SVT}}(r) = V_\infty \cdot \sqrt{\ln\left(1 + \frac{r}{r_c}\right)} \cdot \left[\ln\left(1 + \frac{M_b}{M_c}\right)\right]^{1/4}$$

Where:

• $V_\infty$ = asymptotic velocity scale (related to vacuum sound speed)
• $r_c$ = core radius (effective healing length at galactic scales)
• $M_b$ = total baryonic mass
• $M_c \sim 10^6 M_\odot$ = critical mass scale

Vortex–Black Hole Correspondence

Superfluid Vortex	Black Hole
Vortex core (ρ = 0)	Singularity
Ergosphere (v = cₛ)	Event horizon
Winding number n	Angular momentum J = nℏ
Vortex energy E	Mass M = E/c²
Healing length ξ	Planck length ℓₚₗ

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📊 Key Results

SPARC Database Validation

Tested against 175 galaxies from the SPARC (Spitzer Photometry and Accurate Rotation Curves) database:

Metric	SVT	NFW (ΛCDM)
Median χ²ᵥ	2.53	2.37
Mean χ²ᵥ	10.48	10.90
Excellent fits (χ²ᵥ < 1)	25.7%	30.4%
Good fits (χ²ᵥ < 2)	42.7%	46.8%
Head-to-head wins	50.9%	49.1%

Conclusion: SVT achieves statistical parity with the standard dark matter model while requiring no invisible particles.

Visual Results

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✨ What This Framework Explains Naturally

Observation	ΛCDM Explanation	SVT Explanation
Flat rotation curves	Dark matter particles	Vacuum vortex energy
Baryonic Tully-Fisher Relation (V⁴ ∝ M)	Fine-tuned feedback	Built into mass factor
M–σ relation	Co-evolution	Topological unity
Ubiquity of SMBHs	Evolutionary coincidence	Topological necessity
Core-cusp problem	Requires baryonic feedback	Naturally cored profiles
Radial Acceleration Relation	Coincidental	Fundamental

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📁 Repository Structure

SVT-Galaxy-Rotation-Curves/
├── README.md                        # This file
├── model_fitter.py                  # Main fitting code for SVT and NFW models
├── galaxy_chi2_comparison.csv       # Chi-squared results for all 175 galaxies
├── final_showdown.png               # SVT vs NFW comparison visualization
├── svt_parameter_universality.png   # Parameter distribution analysis
├── galaxy_fits/                     # Individual galaxy rotation curve fits
│   └── [galaxy_name].png            # Fit plots for each SPARC galaxy
└── sparc_data/
    └── sparc_database/              # SPARC galaxy database files
        └── [galaxy_name].txt        # Rotation curve data for each galaxy

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🚀 Installation

git clone https://github.com/wohlig/SVT-Galaxy-Rotation-Curves.git
cd SVT-Galaxy-Rotation-Curves
pip install numpy scipy matplotlib pandas

Dependencies

• Python 3.8+
• NumPy
• SciPy
• Matplotlib
• Pandas

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💻 Usage

Running the Model Fitter

python model_fitter.py

This will:

1. Load all SPARC galaxy data
2. Fit both SVT and NFW models to each galaxy
3. Generate comparison plots in galaxy_fits/
4. Output statistics to galaxy_chi2_comparison.csv

Basic SVT Rotation Curve Calculation

import numpy as np

def V_svt(r, V_infty, r_c, M_bary):
    """
    SVT rotation curve from Logarithmic Superfluid Vacuum.
    
    Parameters:
        r       : Radius array (kpc)
        V_infty : Asymptotic velocity scale (km/s)
        r_c     : Core radius (kpc)
        M_bary  : Baryonic mass (solar masses)
    
    Returns:
        Vacuum contribution to rotation velocity (km/s)
    """
    M_crit = 1.0e6   # Critical mass (solar masses)
    R_norm = 50.0    # Normalization radius (kpc)
    
    # Spatial profile (logarithmic)
    spatial = np.sqrt(np.log(1 + r / r_c))
    norm = np.sqrt(np.log(1 + R_norm / r_c))
    
    # Mass factor (BTFR scaling)
    mass_factor = np.log(1 + M_bary / M_crit)**0.25
    
    return V_infty * (spatial / norm) * mass_factor


# Example: Calculate rotation curve
r = np.linspace(0.1, 30, 100)  # radius in kpc
V_infty = 150                   # km/s
r_c = 3.0                       # kpc
M_bary = 1e10                   # solar masses

v_svt = V_svt(r, V_infty, r_c, M_bary)

Total Rotation Velocity

def V_total(r, V_gas, V_disk, V_bulge, V_infty, r_c, M_bary):
    """
    Total rotation velocity combining baryonic and SVT components.
    """
    V_bary = np.sqrt(V_gas**2 + V_disk**2 + V_bulge**2)
    V_halo = V_svt(r, V_infty, r_c, M_bary)
    return np.sqrt(V_bary**2 + V_halo**2)

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🔮 Predictions

The SVT framework makes testable predictions:

1. No direct detection: Dark matter particle searches will continue to yield null results
2. Tighter M–σ relation: Black hole mass and halo properties should correlate more tightly than ΛCDM predicts
3. No orphan halos: Dark matter halos without associated galaxies and central black holes should not exist
4. Universal vacuum parameters: V∞ and rᶜ should show systematic trends across galaxy types

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📚 Related Papers

1. Vortex–Black Hole Correspondence: DOI: 10.5281/zenodo.18144224

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📖 Citation

If you use this code or find our work useful, please cite:

@article{shah2026svt_unified,
  title={Galaxy Rotation Curves from Superfluid Vacuum Theory: A Unified Framework Integrating the Vortex–Black Hole Correspondence},
  author={Shah, Chintan},
  year={2026},
  doi={10.5281/zenodo.18150850},
  url={https://doi.org/10.5281/zenodo.18150850}
}

@article{shah2026vortex_bh,
  title={Quantum Vortices as Black Hole Analogs in Logarithmic Superfluid Vacuum Theory},
  author={Shah, Chintan},
  year={2026},
  doi={10.5281/zenodo.18144224},
  url={https://doi.org/10.5281/zenodo.18144224}
}

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🔗 References

• SPARC Database: Lelli, McGaugh & Schombert (2016)
• Logarithmic Quantum Mechanics: Białynicki-Birula & Mycielski (1976)
• Superfluid Vacuum Theory: Volovik (2003), Zloshchastiev (2011, 2018, 2023)
• Analog Gravity: Unruh (1981), Barceló, Liberati & Visser (2005)

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📜 License

This project is licensed under the MIT License - see the LICENSE file for details.

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👤 Author

Chintan Shah
University of Mumbai, Mumbai, India 📧 [email protected]
🐙 GitHub: @wohlig

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🙏 Acknowledgments

• The SPARC team for making their galaxy database publicly available
• K. G. Zloshchastiev for foundational work on logarithmic superfluid vacuum theory
• G. E. Volovik for pioneering the superfluid vacuum framework

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"The missing mass is not missing particles — it is the gravitating energy of the vacuum's topological configuration."