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•Mixed-mode coupling strength measured by coupling factor 𝑞 •Measured red giant core rotation rates ≪ predicted by angular-momentum transport models (Hekker & Christensen-Dalsgaard, 2017) Mixed-mode coupling factor as a probe of rotation at the base of the convective envelope of red giants Wei Qiang1,2, Lisa Bugnet2, Stéphane Mathis3, Andrei-Alexandru Cristea2, Lucas Barrault2, Ankit Saha2 1University of Oxford 2Institute of Science and Technology Austria 3CEA Paris-Saclay Dispersion relation: short-wavelength equatorial wave using Cowling approximation & JWKB approximation, in line with Ando (1981, 1985) where 𝑆𝑙 2= 𝑙2𝑐𝑠 2/𝑟2, 𝑙2= 𝑘2+ 𝑚2, 𝜁 = 1 𝑟 d 𝑟2Ω d𝑟 Figure 2. Properties of the stellar models used: their positions on the evolution track, radial profiles of the frequencies, and the applicable formalism(s). EZ is bounded between where 𝑁, 𝑆1= 𝜈max. With rotation •Change in 𝑞 ~ 0.00004-0.0007 ≪ detection resolution ~ 0.01 ⇒ Not very possible to measure Ω from 𝑞 •Further study to link the single 𝑞 observed to the multiple 𝑞 in model Aiming to better understand the angular momentum transport in red giants, we computed the mixed-mode coupling factor of three red giant models at different stages of evolution with a range of rotation rates, which showed the possibility of constraining red giant rotation at the core/envelope boundary from the coupling factor is small. Ando H., 1981, MNRAS, 197, 1139 Ando H., 1985, PASJ, 37, 47 Hekker S., Christensen-Dalsgaard J., 2017, A&ARv, 25, 1 Li G., Deheuvels S., Ballot J., 2024, A&A, 688, A184 Mosser B., et al., 2017, A&A, 600, A1 Pinçon C., Goupil M.J., Belkacem K., 2020, A&A, 634,A68 Shibahashi H., 1979, PASJ, 31, 87 Takata M., 2016, PASJ, 68, 109 Unno W., et al., 1989, Nonradial oscillations of stars, 2 edn. University of Tokyo Press Results Conclusion References Without rotation •𝑞 matched the observed value range for both formalisms 𝑟/𝑅∗ Ω [𝜇Hz] Ωc 1 Ωc− 1 0 Convective gravity modes Radiative pressure modes Evanescent zone (EZ) (where modes couple) Applied to stellar models •Star A, B, C: young, evolving, evolved 1.5𝑀⊙ red giant •Computed their 𝑞 when rotating at 3 types of Ω 𝑟 for Ωc∈ 0,3 𝜇Hz: S79 & T16 applicable S79 applicable S79 applicable 𝑘𝑟 2=𝜔2− 𝑆𝑙 2 𝑐𝑠 21 + 𝑟2𝜁2 𝑚2𝑐𝑠 2+𝜁 𝑚𝜔 dln 𝜁 dln 𝑟− 1 − 2𝑁2𝑟 𝑔𝑒 −dln 𝜌 dln 𝑟−𝑁2 𝜔2−𝑘2𝜁2 𝑚2𝜔2 Formalisms to calculate 𝑞 •Shibahashi (1979) (hereafter S79): thick evanescent zone (EZ) •Takata (2016) (hereafter T16): very thin evanescent zone PRELIMINARY Qiang et al. (in prep) Figure 1. Schematic diagram of the structure and oscillation modes of red giants Introduction Can we probe rotation here (at EZ) from 𝑞? Methods Aim to evaluate the effect of rotation on 𝑞
