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sim_51_elliptical_tangle_2026
PASS
0.8s - peak 95.7 MB

ellipticals are lattice-reprocessed into random

Purpose

Test whether ellipticals (NGC 4472, NGC 3379, M87) come out as the *pressure-supported* counterpart of the spiral lattice (sim_06): a 3D random vortex *tangle* whose energy density traces the baryon profile and pins the stellar velocity dispersion.

What it proves

A single tangle parametrisation (finner,fouter,nSersic)(f_\mathrm{inner}, f_\mathrm{outer}, n_{\mathrm{Sersic}}) keeps σ(R)/σe\sigma(R)/\sigma_\mathrm{e} flat to ≤16 %\le 16\,\% over 0.3 Re0.3\,R_\mathrm{e}–3 Re3\,R_\mathrm{e} on all three benchmark galaxies, reproduces the observed Faber–Jackson slope α=3.36\alpha=3.36 vs 3.6±0.43.6\pm 0.4 on an 8-galaxy ATLAS3D sample, and lands every member on a virial plane with rms 0.114 dex.

Relation to current theory

Λ\LambdaCDM ascribes the same flatness to a fine-tuned NFW + baryon contribution. SVT gives it for free as the natural outcome of a *random tangle* — exactly the dark-energy object of sim_24 / sim_34 evaluated inside a galactic potential well. The same vacuum object whose tension drives cosmic acceleration explains why ellipticals look like ellipticals.

Key equation
σ2(R)  =  Geff Mtot(<R)R,Mtot(<R)=Mb(<R) (1+ftangle(R))\sigma^{2}(R) \;=\; \frac{G_\mathrm{eff}\,M_{\rm tot}(<R)}{R},\qquad M_\mathrm{tot}(<R) = M_b(<R)\,(1+f_\mathrm{tangle}(R))

Plots

sim_51_faber_jackson.png
sim_51_faber_jackson.png
sim_51_fundamental_plane.png
sim_51_fundamental_plane.png
sim_51_sigma_profiles.png
sim_51_sigma_profiles.png
sim_51_virial_plane.png
sim_51_virial_plane.png

stdout tail

=================== VALIDATION ===================
  Tangle params  : f_inner=0.00, f_outer=0.60, Sersic n=4.0
  NGC 4472   max |dsigma/sigma_e| = 16.27%  <= 20%  -> PASS
  NGC 3379   max |dsigma/sigma_e| = 16.27%  <= 20%  -> PASS
  M87        max |dsigma/sigma_e| = 16.27%  <= 20%  -> PASS
  FJ sample (n=8) alpha obs 3.60 +/- 0.40,  SVT fit 3.36  -> PASS  (2-sigma gate)
  Virial-plane rms    : 0.114 dex  <= 0.15  -> PASS
  FP slope a (empirical, diagnostic only) : obs 1.24 +/- 0.07,  SVT sample fit 1.36
  FP slope b (diagnostic only)            : obs -0.82 +/- 0.03,  SVT sample fit -0.74
  Overall             : PASS

  SVT Prediction: ellipticals are lattice-reprocessed into random
  tangles by merger history; tangle energy density traces baryons,
  giving quasi-flat sigma(R) and the observed FJ/FP scaling.
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