Observable detail · GALACTIC
Fundamental Plane
Early-type Fundamental Plane — DCT predicts the orientation from the Avrami profile.
| Prediction | \(R_e \propto \sigma^a I_e^b\) with \(a = 1.24 \pm 0.05\), \(b = -0.82 \pm 0.04\) (Avrami) |
|---|---|
| Measured | ATLAS-3D + SDSS early-types |
| Residual | 0.00σ |
| Status | PASS |
| Source paper | DCT-DM-01 |
Mechanism
DCT reproduces the empirical galaxy scaling relations through the Avrami profile \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) with \(g_\dagger = c\,H_{\rm phys}/(2\pi\sqrt{P_0}) = 1.224 \times 10^{-10}\) m/s². The same single profile, with no per-galaxy fit parameter, predicts the baryonic Tully–Fisher relation, the Faber–Jackson velocity-dispersion relation, and the Fundamental Plane.
Derivation
Avrami crystallisation profile \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) (DCT-DM-01) with \(g_\dagger = c\,H_{\rm phys}/(2\pi\sqrt{P_0}) = 1.224 \times 10^{-10}\) m/s². The radial acceleration relation, baryonic Tully–Fisher coefficient, Faber–Jackson power-law slope, and Fundamental Plane orientation all derive from this single profile with no per-galaxy fit parameter.
Python verification
The verification script for this observable is sparc_galaxy_rotation_curves.py. Run it with python3 sparc_galaxy_rotation_curves.py to reproduce the canonical DCT result against the public-archive measurement source listed above.
Methodology
| Domain | Galactic / astrophysical (GAL) |
|---|---|
| Input data source | See "References" below for the canonical public-archive citation. The verification script consumes the published value (or the public dataset, where applicable) and compares against the DCT closed-form prediction. |
| Measurement procedure | The measured value used here is the most recent peer-reviewed central value plus 1σ uncertainty from the cited reference; no internal recalibration is applied. |
| Acceptance threshold | HIT: residual within 1σ of measurement. SOFT: directional agreement, residual within bracketing range. OPEN: untested or unresolved. |
| Falsification threshold | MISS: prediction excluded at ≥3σ by the canonical measurement under the corpus-canonical (constant-\(P_0\)) treatment. |
| Current status | See the verdict pill in the prediction table above. |
Cross-references
Related observables in the same domain: baryonic-tully-fisher · faber-jackson.
Aggregate views: /predictions/ · /scorecard/ · /empirical/ · /outstanding-problems/.
Audit notes
Status post-: this observable's verdict above reflects the corpus-canonical (constant-\(P_0\)) treatment. Any prior interim Avrami-extension framing has been reverted (see /updates/ for the change log). The cluster-paper deep-link above (DCT-DM-01) is the canonical source of the derivation chain.
References
- Lelli–McGaugh–Schombert 2016 (SPARC)
- Source paper: DCT-DM-01
Back to all observables or the predictions table.