Faber-Jackson relation

Faber-Jackson velocity-dispersion relation — DCT predicts the slope from g_†.

Prediction	\(L \propto \sigma^4\); slope \(4 \pm 0.05\) from Avrami profile
Measured	ATLAS-3D + SDSS early-types, Cappellari et al.
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 · fundamental-plane.

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

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