The inertial dip as a window on the convective core dynamics

Abstract

Gamma Dor stars are ideal targets for studies of the innermost dynamical properties of stars, due to their rich frequency spectrum of gravito-inertial modes propagating in the radiative envelope. Recent studies found that these modes could couple at the core-to-envelope interface with pure inertial modes in their sub-inertial regime, forming the so-called inertial dip in the period-spacing pattern of these stars. The inertial dip, as formed by core modes, stands out as a unique probe of core properties. We aim in this work to explore the effect of core magnetism on its structure, property of key relevance in modern stellar physics. We describe the outlines of our model and the geometry of the considered field. We give the coupling equation and the variation of the dip shape and location with increasing magnetic contrast between the core and the envelope. We compare our findings to the ones obtained in a hydrodynamical, differentially-rotating case. We show hints at potentially lifting the degeneracy between the signatures of core-to-envelope differential rotation and core magnetic fields. Together, these two cases can be considered as an exploration of different magnetic regimes potentially reached in the core of gamma Dor stars.

Figures (2)

• Figure 1: Left: Magnetic star with a bi-layer Alfvén frequency, $\omega_{\rm A, core}$ in the core, $\omega_{\rm A, env}$ in the envelope, and a bi-layer rotation rate, $\Omega_{\rm core}$ in the core, $\Omega_{\rm env}$ in the envelope. The cavity for $m\text{-}g\text{-}i$ modes lies between $r_{\rm a}$ and $r_{\rm b}$ in the radiative zone. They become evanescent in the region $[R_{\rm core};r_{\rm a}]$ when the TARM is applied. $m\text{-}i$ modes propagate in the convective core below the location $R_{\rm core}$. Extracted from Barrault2025ExploringField. Right: Inertial dips overplotted for different core Lehnert number for a fixed envelope Lehnert number $\rm Le_{env} = 10^{-3}$, in a uniformly rotating star, in the frame co-rotating with the envelope. The dots are obtained by solving the coupling equation numerically, and the continuous line by applying a dip profile given in Barrault2025ExploringField. Adapted from Barrault2025ExploringField.
• Figure 2: Left: Red: Spin parameter of the pure inertial mode in the frame co-rotating with the envelope $s^{*}_{\rm env}$ in the hydrodynamic, differentially-rotating case as function of the amount of differential rotation Barrault2025ConstrainingDips Blue: the magnetic, bi-layer Alfvén frequency case as function of $\rm Le_{core}$Barrault2025ExploringField. Horizontal solid lines correspond to the shift of the dip introduced by the effect of typical magnetostrophic fields in three models: $fz$ fast-rotating ZAMS, $iz$ intermediate rotating ZAMS, $im$ intermediate rotating middle-aged MS stars. Vertical dashed lines intersecting the bottom x-axis correspond to the amount of differential rotation required to produce the same shift in the bi-layer, non magnetic model. Extracted from Barrault2025ExploringField. Right: Sample of $\gamma$ Dor stars containing dips analyzed by Saio2021RotationModes. The x-axis denotes the detected differential rotation between the convective core and the near-core region. The y-axis is the central hydrogen fraction. Different data points for each star represent the results obtained for different prescriptions of core boundary mixing used. Two stars (KIC5985441 and KIC4390625) appear as outliers of the overall distribution. Core field strengths are overlaid on the original figure, denoting the amount of core magnetism able to make the two stars join the bulk of detected core-to-envelope differential rotation. Adapted from Saio2021RotationModes, courtesy MNRAS.