3.3 KiB
Explicit rotating n=3 physical-family control
Branch research/n3-compatible-family-20260919; parent 6d423cb.
This changes experimental physical inputs, not solver equations or production
defaults. It must not be presented as a preconditioner speedup comparison.
The driver normally chooses K for a nonrotating mass-one Lane–Emden star. The sharp gravitational-energy inequality and the steady virial identity require, for n=3 and a nonnegative exact-EOS density,
beta = T/|W| <= [1 - (M_LE(K)/M)^(2/3)]/2.
At exactly M=M_LE(K), nonzero rotation is impossible. An independent DOP853 Lane–Emden integration with five tolerance/step/start controls gives the actual driver's K=0.36393905995216302 a Lane–Emden mass 0.9999999918534539. Thus the numerical K is slightly on the permissible side, but beta cannot exceed approximately 2.71552e-9. The control-to-control mass spread is 1.95e-14; this is a numerical sensitivity observation, not a rigorous interval enclosure. The intended moderate rotation cannot be reached while retaining that essentially critical mass/K combination.
The optional experiment flag --n3-K-factor f multiplies K by a positive
factor, with index required to be exactly three when f differs from one.
The default is one. The analytic seed central density is multiplied by
f^(3/2), keeping its radius equal to the unchanged reference radius. Its
mass becomes approximately f^(3/2), while the target mass remains one.
This is a deliberately off-constraint initial guess, not a density rescaling
during Newton. The public EOS and independent density formulation are unchanged.
The seed's Bernoulli scalar continues to use the target mass; its discrepancy
is part of the initial nonlinear residual and is not hidden by this control.
The bounded first case uses f=.99, J=.035, no central border, the existing gravity-Schur preconditioner and gravity-curvature trial path, 10 updates, eta=.03 and absolute nonlinear target 1e-12. The necessary beta bound is then 0.00500000269. This does not guarantee existence, convergence, or identify a fraction of critical rotation. J already breaks the nonrotating n=3 homology, so this case does not add an extra central-density phase condition.
Before execution, the favorable frozen n=3 field-feedback result motivates
one matched live companion using stellar-ldu-gravity-schur. It changes only
the inverse and retains the original ten-update budget, eta=.03, trial path
and physical specifications. The pair is versioned on
research/n3-live-field-feedback-20260919; the main convergence report records
the preceding evidence. No success or speedup is assumed from the frozen
eta=.003, J=0, phase-constrained benchmark.
The energy inequality's assumptions are not automatically satisfied by the discrete independent rho/P(h) fields, approximate gravity, or a central artificial forcing. This compatibility argument selects a sensible continuum target; it is not a new density limiter or a substitute for numerical tests.
Primary source: Cheng, Cheng and Lin, equations (1.14)–(1.15) and Theorem 3.1, Expanding solutions near unstable Lane–Emden stars. The displayed beta bound is our consequence of their inequality and 2T+W+3 integral(P)=0. Their G=1 convention matches this diagnostic.
Independent integration evidence is retained in
../../diagnostics/n3_mass_compatibility_2026-09-19/.