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Table 6.

Maximal absolute non-linear frequency shifts as a fraction of the linear inertial-frame angular frequency δ Ω φ , m s Ω φ , i $ \lvert\delta\Omega^s_{\varphi,{\rm m}} \,\,\Omega_{\varphi,\,i}\rvert $ (in parts-per-thousand), zero-point-corrected non-linear combination phases Φ s , 0 s $ \tilde{\Phi}^s_{s,0} $, and expected stationary surface luminosity fluctuation ratios L 2 s / L 1 s $ \lvert{\mathfrak{L}^s_2}\lvert/\lvert{\mathfrak{L}^s_1}\rvert $ and L 3 s / L 1 s $ \lvert{\mathfrak{L}^s_3}\rvert /\lvert{\mathfrak{L}^s_1}\rvert $ for the mode triads listed in Table 4.

Model (n1,  n2,  n3) | δ Ω φ , m s / Ω φ , i | $ \left|\delta\Omega^s_{\varphi,{\rm m}}\displaystyle/\Omega_{\varphi,\,i}\right| $ (ppt) Φ s , 0 s $ \tilde{\Phi}^s_{s,0} $ (rad) L 2 s / L 1 s $ \lvert{\mathfrak{L}^s_2}\rvert /\lvert{\mathfrak{L}^s_1}\rvert $ L 3 s / L 1 s $ \lvert{\mathfrak{L}^s_3}\rvert /\lvert{\mathfrak{L}^s_1}\rvert $
Fiducial (−51, −38, −90) 0.764733 0.21819 0.55605 0.06168
ΔXc,  1 (−20, −13, −58) 0.708263 −0.79901 0.42858 0.03261
(−21, −14, −54) 1.839526 −0.30412 0.65585 0.06390
(−22, −15, −53) 1.283029 0.39313 0.91831 0.08677
(−39, −40, −40) 0.593527 0.11515 0.48298 0.48298
ΔXc,  2(a) (−10, −7, −22) 2.639689 −0.06776 0.32000 0.05700
(−14, −10, −26) 6.021050 0.10383 2.53183 0.14379
ΔXc,  2(b) (−10, −6, −36) 1.589962 −0.44842 0.32190 0.00750
(−12, −8, −23) 0.766883 −0.18324 0.84057 0.08189
(−17, −12, −30) 0.701324 −0.61847 3.08804 0.06054
(−18, −13, −31) 3.238349 0.17297 2.02044 0.04897
ΔMini,  1 (−50, −48, −56) 0.443377 −0.54958 0.79629 0.41179
(−40, −30, −70) 5.086921 0.16921 2.05217 0.20288
ΔXc|Mini (−16, −14, −22) 0.330309 0.09168 0.07627 0.05190
(−17, −13, −29) 2.600074 0.10985 0.29260 0.08237
(−23, −17, −41) 5.594778 0.29998 0.72069 0.08163
ΔMini,  2 (−31, −23, −56) 1.760714 0.61936 0.34623 0.07864
(−32, −24, −58) 3.997386 0.33231 0.48095 0.07250
(−35, −26, −62) 1.832881 −0.81546 0.61223 0.07525
(−36, −27, −63) 3.610779 0.46404 0.30289 0.04729
(−38, −28, −67) 3.885665 −0.44231 0.12459 0.01283

Notes. The mode triads are identified by their g mode radial orders nφ. We define Φ s , 0 s $ \tilde{\Phi}^s_{s,0} $ as Φ s s + ( Δ ϕ s ) 0 $ \tilde{\Phi}^s_{s} + \left(\Delta\phi^s\right)_0 $. The observables L 2 s / L 1 s $ \lvert{\mathfrak{L}^s_2}\rvert / \lvert{\mathfrak{L}^s_1}\rvert $ and L 3 s / L 1 s $ \lvert{\mathfrak{L}^s_3}\rvert /\lvert{\mathfrak{L}^s_1}\rvert $, as well as Φ s s $ \tilde{\Phi}^s_s $, are defined in Eqs. (76) and (82), respectively.

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