The Sobolev–Ozok Lattice (SOL) Model and the Baryonic Tully–Fisher Relation: A First-Principles Match Without Dark-Matter Tuning
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| Lenguaje: | inglés |
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2025
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| _version_ | 1866902053362597888 |
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| author | Ozok, Ozcan |
| author_facet | Ozok, Ozcan |
| contents | <p>This work applies the Sobolev–Ozok Lattice (SOL) model, a discrete Planck-scale spacetime framework, to the baryonic Tully–Fisher relation (BTFR) observed in rotationally supported galaxies. In the SOL approach, large-scale gravitational dynamics emerge from coherence corrections to the Newtonian potential, without introducing dark matter or empirical tuning parameters.</p> <p>A specific coherence mode with index k = 2 produces a scale-invariant, logarithmic correction to the gravitational potential at large radii. This term naturally yields the observed flattening of galaxy rotation curves and predicts a BTFR slope of approximately four from first principles. Using the SPARC database of 175 disk galaxies, we test the SOL prediction against multiple velocity definitions, finding excellent agreement with low scatter and high coefficient of determination values.</p> <p>The analysis includes regression fits, residual studies, and cross-velocity comparisons. The results demonstrate that the SOL framework can account for the BTFR and the shape of galaxy rotation curves in a parameter-free manner, offering a viable alternative to both dark matter halo models and modified gravity theories such as MOND.</p> <p>This dataset and code package provide the numerical results, figures, and plotting scripts necessary to reproduce all analyses in the paper.</p> <p> </p> <div dir="auto"><strong>Decleration of Tools Used:</strong></div> <div dir="auto">This paper was prepared and formatted using Overleaf (LaTeX editor). Text refinement and language polishing were assisted by Overleaf AI Editor. all scientifit content, derivations, and conclusions are original and autored by the undersigned.</div> <div dir="auto"> </div> <div dir="auto"> <p>This paper is part of the Sobolev–Ozok Lattice (SOL) research program.</p> <p><strong>Project webpage (papers, figures, updates):</strong></p> <p><a href="https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/" target="_blank" rel="noopener">https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/</a></p> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16884010 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Sobolev–Ozok Lattice (SOL) Model and the Baryonic Tully–Fisher Relation: A First-Principles Match Without Dark-Matter Tuning Ozok, Ozcan Baryonic Tully–Fisher relation Galaxy rotation curves SPARC database Sobolev–Ozok lattice model Emergent gravity Coherence scaling Modified Newtonian Dynamics Dark matter alternatives Planck-scale spacetime Astrophysical scaling laws Extragalactic astronomy Galactic dynamics Empirical scaling relations Observational cosmology <p>This work applies the Sobolev–Ozok Lattice (SOL) model, a discrete Planck-scale spacetime framework, to the baryonic Tully–Fisher relation (BTFR) observed in rotationally supported galaxies. In the SOL approach, large-scale gravitational dynamics emerge from coherence corrections to the Newtonian potential, without introducing dark matter or empirical tuning parameters.</p> <p>A specific coherence mode with index k = 2 produces a scale-invariant, logarithmic correction to the gravitational potential at large radii. This term naturally yields the observed flattening of galaxy rotation curves and predicts a BTFR slope of approximately four from first principles. Using the SPARC database of 175 disk galaxies, we test the SOL prediction against multiple velocity definitions, finding excellent agreement with low scatter and high coefficient of determination values.</p> <p>The analysis includes regression fits, residual studies, and cross-velocity comparisons. The results demonstrate that the SOL framework can account for the BTFR and the shape of galaxy rotation curves in a parameter-free manner, offering a viable alternative to both dark matter halo models and modified gravity theories such as MOND.</p> <p>This dataset and code package provide the numerical results, figures, and plotting scripts necessary to reproduce all analyses in the paper.</p> <p> </p> <div dir="auto"><strong>Decleration of Tools Used:</strong></div> <div dir="auto">This paper was prepared and formatted using Overleaf (LaTeX editor). Text refinement and language polishing were assisted by Overleaf AI Editor. all scientifit content, derivations, and conclusions are original and autored by the undersigned.</div> <div dir="auto"> </div> <div dir="auto"> <p>This paper is part of the Sobolev–Ozok Lattice (SOL) research program.</p> <p><strong>Project webpage (papers, figures, updates):</strong></p> <p><a href="https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/" target="_blank" rel="noopener">https://ozokozcasol.github.io/Sobolev-Ozok-Lattice/</a></p> </div> |
| title | The Sobolev–Ozok Lattice (SOL) Model and the Baryonic Tully–Fisher Relation: A First-Principles Match Without Dark-Matter Tuning |
| topic | Baryonic Tully–Fisher relation Galaxy rotation curves SPARC database Sobolev–Ozok lattice model Emergent gravity Coherence scaling Modified Newtonian Dynamics Dark matter alternatives Planck-scale spacetime Astrophysical scaling laws Extragalactic astronomy Galactic dynamics Empirical scaling relations Observational cosmology |
| url | https://doi.org/10.5281/zenodo.16884010 |