Oscillations of 2D ESTER models - I. The adiabatic case

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Table 3.

Generalised splittings versus weighted integrals of the rotation profile, and different terms from Eq. (13) for two pairs of prograde and retrograde modes.

Quantity	Solution 1	Solution 2	Solution 3	Solution 4
m	−2	2	−6	6
ω	17.50030	14.69444	20.42777	12.01274
	0.70146		0.70125
	0.70146		0.70095

δω_var/ω	−8.50 × 10⁻¹¹	−5.18 × 10⁻¹¹	−3.42 × 10⁻¹⁰	−1.09 × 10⁻⁶
	2.01 × 10⁻⁷	−9.84 × 10⁻⁸	5.34 × 10⁻⁷	−4.42 × 10⁻⁸
	0.70463	0.70464	0.70438	0.70436
	0.49651	0.49652	0.49615	0.49614
	0.49651	0.49651	0.49615	0.49613
𝒞_±	−0.04586	−0.05856	−0.03770	−0.07873
(𝒞_±Ω_±)^eff	−0.03234	−0.04128	−0.02657	−0.05544
	−0.03232	−0.04126	−0.02656	−0.05545
rest_±	−257.94181	−257.94021	−261.76369	−261.64204

Notes. δω_var/ω corresponds to the relative error on the variational frequency, and is the same error when ω_var is calculated using the approximations in Eqs. (15) and (17). The modes from the second pair, Solutions 3 and 4, are undergoing avoided crossings, whereas the other two modes are not.

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