Finite Saturation of Rotational Offsets in Disk Galaxies — Phase Mixing and the Limits of History Retention in Temporal Membrane Theory
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| Format: | Recurso digital |
| Langue: | japonais |
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2026
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| _version_ | 1866901099225546752 |
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| author | Sato, Tetsuya |
| author_facet | Sato, Tetsuya |
| contents | <p>This note investigates the finite saturation of apparent rotational offsets observed in disk galaxy rotation curves within the framework of Temporal Membrane Theory (TMT).</p> <p>Instead of interpreting rotation curve discrepancies as a consequence of missing mass or modified gravity, the present work reformulates them as effects of observationally reconstructed motion history. In TMT, apparent rotational enhancement arises from the cumulative reconstruction of motion along time-distorted geodesics, while no active mechanism is assumed to reverse or correct past reconstructed histories.</p> <p>Crucially, this accumulation is shown not to diverge indefinitely. Stellar-dynamical processes intrinsic to disk galaxies—such as non-circular motion, velocity dispersion, epicyclic motion, and phase mixing—act as natural relaxation mechanisms that partially redistribute and cancel accumulated contributions. As a result, the retained history and the associated rotational offset necessarily saturate at a finite scale.</p> <p>The paper introduces a minimal time-response representation for history retention, emphasizing that the specific functional form is not essential, while the existence of saturation is robust. This temporal formulation is derived independently from the spatial gradient-based effective expressions used in the main TMT analysis, yet leads to consistent qualitative behavior without parameter tuning.</p> <p>A semi-quantitative example using the well-studied disk galaxy NGC 3198 illustrates how the predicted saturation scale naturally aligns with observed galactic rotation scales. The purpose is not precision fitting, but to demonstrate the structural consistency of the saturation mechanism with real galaxies.</p> <p>This work serves as an independent and complementary derivation of the finite nature of galactic rotation offsets, reinforcing the interpretation of rotation curves as manifestations of time-reconstructed motion histories rather than evidence for additional gravitational sources.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18503118 |
| institution | Zenodo |
| language | jpn |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Finite Saturation of Rotational Offsets in Disk Galaxies — Phase Mixing and the Limits of History Retention in Temporal Membrane Theory Sato, Tetsuya Temporal Membrane Theory galaxy rotation curves phase mixing history retention observational time reconstruction <p>This note investigates the finite saturation of apparent rotational offsets observed in disk galaxy rotation curves within the framework of Temporal Membrane Theory (TMT).</p> <p>Instead of interpreting rotation curve discrepancies as a consequence of missing mass or modified gravity, the present work reformulates them as effects of observationally reconstructed motion history. In TMT, apparent rotational enhancement arises from the cumulative reconstruction of motion along time-distorted geodesics, while no active mechanism is assumed to reverse or correct past reconstructed histories.</p> <p>Crucially, this accumulation is shown not to diverge indefinitely. Stellar-dynamical processes intrinsic to disk galaxies—such as non-circular motion, velocity dispersion, epicyclic motion, and phase mixing—act as natural relaxation mechanisms that partially redistribute and cancel accumulated contributions. As a result, the retained history and the associated rotational offset necessarily saturate at a finite scale.</p> <p>The paper introduces a minimal time-response representation for history retention, emphasizing that the specific functional form is not essential, while the existence of saturation is robust. This temporal formulation is derived independently from the spatial gradient-based effective expressions used in the main TMT analysis, yet leads to consistent qualitative behavior without parameter tuning.</p> <p>A semi-quantitative example using the well-studied disk galaxy NGC 3198 illustrates how the predicted saturation scale naturally aligns with observed galactic rotation scales. The purpose is not precision fitting, but to demonstrate the structural consistency of the saturation mechanism with real galaxies.</p> <p>This work serves as an independent and complementary derivation of the finite nature of galactic rotation offsets, reinforcing the interpretation of rotation curves as manifestations of time-reconstructed motion histories rather than evidence for additional gravitational sources.</p> |
| title | Finite Saturation of Rotational Offsets in Disk Galaxies — Phase Mixing and the Limits of History Retention in Temporal Membrane Theory |
| topic | Temporal Membrane Theory galaxy rotation curves phase mixing history retention observational time reconstruction |
| url | https://doi.org/10.5281/zenodo.18503118 |