The Temporal Architecture of Disc Galaxy Assembly: Morphological Fossilization and the Selective Extinction of the Fall Relation

The Σ-A/B/C/D disc sequence identified empirically in Houart (2026a, H26a) via Gaussian Mixture Model (GMM) classification on baryonic mass Mbar, surface density Σbar, and gas fraction fgas, and whose kinematic origin in angular-momentum-driven inside-out growth was established in Houart (2026b, H26b), is shown here to possess a temporal architecture with two independent degrees of freedom. We combine IFU spectroscopy from MaNGA (N = 982), cosmological merger trees from TNG100 (SubLink, N = 92 Σ-A progenitors over ten snapshots z = 5.23 → 0), and GMM cross-validation in EAGLE RefL0100N1504 to establish one central result and three supporting findings. Central result: Within the disc-dominated sub-population (X2: n ≤ 3.5), the angular-momentum–morphology coupling (Fall coupling) ρ∂(jbar, n | M) is active (−0.35∗∗∗ to −0.39∗∗∗), and is completely extinct in the fossilized sub-population (X1: ρ ≈ 0 ns; Fisher z: p = 0.019∗ and 0.035∗ for Σ-A and Σ-B), confirmed by seven independent robustness tests. The Sérsic index n loses all predictive power with respect to 11 observables in X1 (all |ρ| < 0.25 ns), and ρ(n,Dn4000) reverses sign from +0.481∗∗∗ in X2 to −0.094 ns in X1 (p = 0.0001∗∗∗): a morphological fossilization event. Supporting findings. (i) [TNG100] The three kinematic families Σ-A, Σ-B, Σ-C are already separable at the earliest surveyed TNG100 snapshot (z ≈ 5, Kruskal–Wallis p < 10−6), and the Σ-sequence constitutes a temporal sequence of baryonic compaction in TNG100: Σbar peaks at z = 3.01 for Σ-A and z = 2.00 for Σ-B/C, with a simulation-based timing gap of Δt = 1.19 ± 0.31 Gyr (these redshifts are TNG-specific). (ii) Two quasi-independent degrees of freedom structure disc galaxy assembly: a kinematic axis (β, jbar, Rd; inside-out disc growth) and a morphological axis (Sérsic n, Dn4000, g − r, sSFR), sharing only 4.2% of variance (H26a; bivariate ρS(n, β) = −0.020 ns, 95%CI [−0.165,+0.130]). (iii)Within both Σ-A and Σ-B, the bulge-dominated sub-population (X1: n > 3.5) is kinematically indistinguishable from the disc-dominated sub-population (X2: n ≤ 3.5) (|β|, Rd, jbar: all Cohen |d| < 0.30, ns), yet assembles its stellar mass 3.57 Gyr earlier in Σ-A (p = 0.003) and 2.73 Gyr earlier in Σ-B (p = 0.028). More fundamentally, X1 galaxies undergo morphological fossilization: within X1, the Sérsic index n loses all predictive power with respect to 11 tested observables (all |ρ| < 0.25, all ns; 95% confidence intervals exclude ρ = −0.45 for all three key variables: Dn4000 CI= [−0.33,+0.15], sSFR CI= [−0.42,+0.04], fgas CI= [−0.35,+0.13], confirming the null is not a power artefact), and the Fall angular-momentum–morphology coupling ρ∂(jbar, n | M) is completely extinct (Σ-A X1: ρ = −0.054 ns; Σ-B X1: ρ = −0.010 ns; Fisher z: p = 0.019∗ and 0.035∗ respectively). The sign of ρ(n,Dn4000) reverses from +0.481∗∗∗ in X2 to −0.094 ns in X1 (p = 0.0001∗∗∗), identifying a topological change in the galaxy correlation network. The second degree of freedom thus does not simply encode assembly epoch — it marks a continuous transition from an evolutionary regime (X2: n is a live state tracer, Fall coupling active ρ = −0.39∗∗∗) to a fossil regime (X1: n is decoupled from all current physics, Fall coupling extinct ρ ≈ 0). The fossilization signal first becomes detectable at n ≈ 3.5 and peaks near n ≈ 4.5; the n = 3.5 boundary is therefore an operational detection threshold, not a fundamental physical discontinuity. The transition is progressive—referees wishing to verify this are referred to the threshold sweep test in Sect. 5.6. (iv) A fifth GMM component (k = 5, ΔBIC = −401 to −2173 from z = 0 to z = 2 in EAGLE) spontaneously reproduces the H26a D1/D2 dwarf bimodality (ΔBIC = −25.5 in observations) and reveals a systematic migration from the gas-rich D1 regime (58% at z = 2) to the transitional D2 regime (30% at z = 0), establishing the D1/D2 dichotomy as an ancient and cosmologically persistent bifurcation.