Formation-Epoch Dependence of Stellar Velocity-Dispersion Residuals in 8,395 MaNGA Early-Type Galaxies

Abstract

If present-day stellar mass, size, and morphology fully determine the dynamics of early-type galaxies, residuals around the Faber–Jackson relation should carry no memory of when a galaxy formed. This paper characterises that memory. A fixed OLS regression with HC3 robust standard errors is fit to N=8,395 MaNGA DR17 early-type galaxies, regressing Faber–Jackson residuals on the formation-epoch coupling function W(z_form)=z_form/(1+z_form) with stellar mass, Sérsic index, and effective radius as controls; the full specification was fixed in advance of the corrected primary analysis reported here, and the revision corrects an implementation inconsistency in the originally submitted sample construction. The formation-epoch slope is β_W = +0.0949±0.0223 dex per unit W (t=4.25, p=2.1×10⁻⁵; model-free permutation test p<10⁻⁴, Z=5.2σ). The detection is statistically decisive but physically modest: adding W raises R² by only 0.0023 and the partial correlation is r=+0.053 (r²≈0.003), so formation epoch is a small, highly significant modulation of the residuals, not a dominant driver. The signal is insensitive to the σ quality cut: the superseded construction yields a slope within 0.9σ of the value reported here. A metallicity control attenuates the slope, the coefficient is strongly age-proxy-dependent, and controlling for Sérsic n attenuates but does not absorb it. The amplitude, a raw quintile progression of 0.12 dex and a fully-controlled slope of 0.09 dex per unit W, is consistent in scale with direct stellar-population age-residual measurements of the fundamental plane and Faber–Jackson relations; matched simulation comparisons place the slope within the span of ΛCDM assembly-history measurements in IllustrisTNG and EAGLE, and a fully specification-matched particle-level IllustrisTNG measurement, performed for this revision, reproduces it, consistent with matched ΛCDM assembly-history expectations. The sign of the effect is consistent with Looped Spacetime Cosmology (LSC; a single closed spacetime, not a cyclic succession of universes), offered here as an interpretive hypothesis in which the BH→BB topological identification on a compact S³×S¹ spacetime acts as an emergent, age-dependent halo response; a logically independent set of secondary cosmological analyses bounds the theory's backreaction channel. At the amplitude detected here, present-day stellar mass, morphology, and size do not fully account for early-type kinematic structure.