Understanding how angular momentum and chemicals are transported in the interiors of stars (and planets) along their evolution is one of the key challenges of modern stellar (and planetary) astrophysics. Indeed, rotation modifies their structure, their chemical stratification, their internal flows and magnetism, and their mass losses and winds (e.g. Maeder 2009; Mathis et al. 2013; Aerts et al. 2019, and references therein). In this quest, asteroseismology has bought a fundamental breakthrough by demonstrating that all stars are the seat of a strong extraction of angular momentum during their evolution in comparison with the predictions by stellar models taking the rotation into account following the standard rotational transport and mixing theory (Eggenberger et al. 2012; Marques et al. 2013; Ceillier et al. 2013; Cantiello et al. 2014; Ouazzani et al. 2019). This was first obtained thanks to mixed pulsation modes splitted by rotation propagating in evolved low- and intermediate-mass stars (Beck et al. 2012, 2014, 2018; Mosser et al. 2012; Deheuvels et al. 2012, 2014, 2015; Deheuvels et al. 2020; Di Mauro et al. 2016; Triana et al. 2017; Gehan et al. 2018; Tayar et al. 2019). Then, observations of oscillation modes in F- and A-type stars (Kurtz et al. 2014; Saio et al. 2015; Bedding et al. 2015; Keen et al. 2015; Van Reeth et al. 2015, 2016, 2018; Schmid & Aerts 2016; Murphy et al. 2016; Sowicka et al. 2017; Guo et al. 2017; Saio et al. 2018, 2021; Mombarg et al. 2019; Li et al. 2019, 2020; Ouazzani et al. 2020) and in B-type stars (Pápics et al. 2015, 2017; Triana et al. 2015; Moravveji et al. 2016; Kallinger et al. 2017; Buysschaert et al. 2018; Szewczuk & Daszyńska-Daszkiewicz 2018; Pedersen et al. 2021; Szewczuk et al. 2021) provided us new Rosetta stones to constrain the transport of angular momentum in the whole Hertzsprung-Russell diagram. More particularly, this pushes gravity- and gravito-inertial mode pulsators such as γ-Doradus and SPB stars at the forefront of this research. For instance, recent theoretical developments have demonstrated how it is possible to probe stellar internal rotation in γ-Doradus stars from their surface to their convective core (Ouazzani et al. 2020; Saio et al. 2021). These stars are rapid rotators for a large proportion of them. Therefore, it is necessary to study gravito-inertial modes. These modes are gravity modes, which propagate only in stably stratified stellar radiation zones under the action of the restoring buoyancy force in the absence of rotation, which are modified by rotation. If their frequency is super-inertial (i.e. above the inertial frequency 2Ω, Ω being the stellar angular velocity), they are propagating in stellar radiation zones and evanescent in convective regions. If their frequency is sub-inertial (below 2Ω) they propagate in an equatorial belt in radiation zones and they become propagative inertial waves in convective regions (e.g. Dintrans & Rieutord 2000; Mathis et al. 2014). The challenge of studying these waves is that the equation describing their dynamics are intrinsically bi-dimensional and non-separable (Dintrans et al. 1999; Prat et al. 2016, 2018; Mirouh et al. 2016). This makes the development of seismic diagnosis difficult analytically (Prat et al. 2017) or expansive in computation time when using 2D oscillation and stellar structure codes (e.g. Ouazzani et al. 2017; Reese et al. 2021) in the general case.
Citation: Triana et al. 2015
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