Top: integrated kernel (β I) with β and I given by Eqs. (13) and (8) respectively, (blue dotted line, dots correspond to modes) and mode inertia I (red dotted line, dots correspond to modes) in decimal logarithm for model M1. Black crosses represent the inertia of radial modes. Bottom: rotational splittings (Eq. (11)), in μHz, for ℓ = 1 modes as a function of the normalized frequency ν/Δν for M1 (black dots connected by a dotted line). The magenta open dots connected with the magenta dotted line represents the core contribution to the rotational splittings  ⟨ Ω ⟩ _coreβ_core (Eqs. (15) and (18)). The core contribution to the rotational splittings (Eq. (15)) with  ⟨ Ω ⟩ _core computed with the horizontal eigenfunction z₂ alone is displayed with the blue crosses dotted line. The blue dotted line represents the contribution from the envelope to the rotational splittings  ⟨ Ω ⟩ _env (β − β_core). The value  ⟨ Ω ⟩ _core/4π is drawn with the horizontal red dotted line.