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Solar Inertial Modes

Published online by Cambridge University Press:  23 December 2024

Laurent Gizon Open the ORCID record for Laurent Gizon [Opens in a new window] ,
Yuto Bekki ,
Aaron C. Birch ,
Robert H. Cameron ,
Damien Fournier ,
Jordan Philidet ,
B. Lekshmi Open the ORCID record for B. Lekshmi [Opens in a new window]  and
Zhi–Chao Liang Open the ORCID record for Zhi–Chao Liang [Opens in a new window]
Laurent Gizon*
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany Institut für Astrophysik und Geophysik, Georg–August-Universität Göttingen, Germany
Yuto Bekki
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany
Aaron C. Birch
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany
Robert H. Cameron
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany
Damien Fournier
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany
Jordan Philidet
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany
B. Lekshmi
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany
Zhi–Chao Liang
Affiliation:
Max–Planck-Institut für Sonnensystemforschung, Göttingen, Germany
*
email: gizon@mps.mpg.de
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Abstract

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The Sun’s global inertial modes are very sensitive to the solar differential rotation and to properties of the deep solar convection zone which are currently poorly constrained. These properties include the superadiabatic temperature gradient, the latitudinal entropy gradient, and the turbulent viscosity. The inertial modes also play a key role in controlling the Sun’s large-scale structure and dynamics, in particular the solar differential rotation. This paper summarizes recent observations and advances in the (linear and nonlinear) modeling of the solar inertial modes.

Keywords

Solar inertial modessolar rotationsolar convection
Type
Contributed Paper
Information
Proceedings of the International Astronomical Union , Volume 19 , Symposium S365: Dynamics of Solar and Stellar Convection Zones and Atmospheres , December 2023 , pp. 207 - 221
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of International Astronomical Union

References

Balmforth, N. J. and Morrison, P. J. (1995). Normal modes and continuous spectra. Ann. New York Acad. Sci., 773:80–94.CrossRefGoogle Scholar
Baruteau, C. and Rieutord, M. (2013). Inertial waves in a differentially rotating spherical shell. J. Fluid Mech., 719:47–81.CrossRefGoogle Scholar
Bekki, Y. (2024). Numerical study of non-toroidal inertial modes with l = m + 1 radial vorticity in the Sun’s convection zone. Astron. Astrophys., 682:A39.CrossRefGoogle Scholar
Bekki, Y., Cameron, R. H., and Gizon, L. (2022a). Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation. Astron. Astrophys., 666:A135.CrossRefGoogle Scholar
Bekki, Y., Cameron, R. H., and Gizon, L. (2022b). Theory of solar oscillations in the inertial frequency range: Linear modes of the convection zone. Astron. Astrophys., 662:A16.CrossRefGoogle Scholar
Bekki, Y., Cameron, R. H., and Gizon, L. (2024). The Sun’s differential rotation is controlled by high-latitude baroclinically unstable inertial modes. Science Adv., accepted.CrossRefGoogle Scholar
Bhattacharya, J. and Hanasoge, S. M. (2023). A Spectral Solver for Solar Inertial Waves. Astrophys. J. Suppl. Ser., 264(1):21.CrossRefGoogle Scholar
Birch, A. (2023). Convection spectra from the thesis of B. Proxauf, https://doi.org/10.17617/3.DFU3SQ.CrossRefGoogle Scholar
Blume, C. C., Hindman, B. W., and Matilsky, L. I. (2023). Inertial Waves in a Nonlinear Simulation of the Sun’s Convection Zone and Radiative Interior, doi: 10.48550/arxiv.2312.14270.CrossRefGoogle Scholar
Charbonneau, P., Dikpati, M., and Gilman, P. A. (1999). Stability of the Solar Latitudinal Differential Rotation Inferred from Helioseismic Data. Astrophys. J., 526(1):523–537.CrossRefGoogle Scholar
Damiani, C., Cameron, R. H., Birch, A. C., and Gizon, L. (2020). Rossby modes in slowly rotating stars: depth dependence in distorted polytropes with uniform rotation. Astron. Astrophys., 637:A65.CrossRefGoogle Scholar
Dey, P., Bekki, Y., and Gizon, L. (2024). Probing the superadiabaticity of the solar convection zone with inertial modes. In this volume.Google Scholar
Dikpati, M., McIntosh, S. W., Bothun, G., Cally, P. S., Ghosh, S. S., Gilman, P. A., and Umurhan, O. M. (2018). Role of Interaction between Magnetic Rossby Waves and Tachocline Differential Rotation in Producing Solar Seasons. Astrophys. J., 853(2):144.CrossRefGoogle Scholar
Drazin, P. G. and Reid, W. H. (2004). Hydrodynamic Stability. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Fournier, D., Gizon, L., and Hyest, L. (2022). Viscous inertial modes on a differentially rotating sphere: Comparison with solar observations. Astron. Astrophys., 664:A6.CrossRefGoogle Scholar
Gilman, P. A. (1977). Nonlinear Dynamics of Boussinesq Convection in a Deep Rotating Spherical Shell. I. Geophys. Astrophys. Fluid Dyn., 8:93–135.CrossRefGoogle Scholar
Gizon, L. and Birch, A. C. (2012). Helioseismology challenges models of solar convection. Proc. Nat. Acad. Sci., 109(30):11896–11897.CrossRefGoogle ScholarPubMed
Gizon, L., Cameron, R. H., Bekki, Y., Birch, A. C., Bogart, R. S., Brun, A. S., Damiani, C., Fournier, D., Hyest, L., Jain, K., Lekshmi, B., Liang, Z.-C., and Proxauf, B. (2021). Solar inertial modes: Observations, identification, and diagnostic promise. Astron. Astrophys., 652:L6.CrossRefGoogle Scholar
Gizon, L., Fournier, D., and Albekioni, M. (2020). Effect of latitudinal differential rotation on solar Rossby waves: Critical layers, eigenfunctions, and momentum fluxes in the equatorial β plane. Astron. Astrophys., 642:A178.CrossRefGoogle Scholar
Glatzmaier, G. A. and Gilman, P. A. (1981). Compressible Convection in a Rotating Spherical Shell - Part Three - Analytic Model for Compressible Vorticity Waves. Astrophys. J. Suppl. Ser., 45:381.CrossRefGoogle Scholar
Goddard, C. R., Birch, A. C., Fournier, D., and Gizon, L. (2020). Predicting frequency changes of global-scale solar Rossby modes due to solar cycle changes in internal rotation. Astron. Astrophys., 640:L10.CrossRefGoogle Scholar
Goldreich, P. and Keeley, D. A. (1977). Solar seismology. II. The stochastic excitation of the solar p-modes by turbulent convection. Astrophys. J., 212:243–251.CrossRefGoogle Scholar
Hanasoge, S. M., Duvall, T. L., and Sreenivasan, K. R. (2012). Anomalously weak solar convection. Proc. Nat. Acad. Sci., 109(30):11928–11932.CrossRefGoogle ScholarPubMed
Hanson, C. S., Hanasoge, S., and Sreenivasan, K. R. (2022). Discovery of high-frequency retrograde vorticity waves in the Sun. Nature Astron., 6:708–714.CrossRefGoogle Scholar
Hathaway, D. H., Upton, L., and Colegrove, O. (2013). Giant Convection Cells Found on the Sun. Science, 342(6163):1217–1219.CrossRefGoogle ScholarPubMed
Hindman, B. W. and Jain, R. (2022). Radial Trapping of Thermal Rossby Waves within the Convection Zones of Low-mass Stars. Astrophys. J., 932(1):68.CrossRefGoogle Scholar
Hotta, H., Kusano, K., and Shimada, R. (2022). Generation of Solar-like Differential Rotation. Astrophys. J., 933(2):199.CrossRefGoogle Scholar
Jain, R. and Hindman, B. W. (2023). Latitudinal Propagation of Thermal Rossby Waves in Stellar Convection Zones. Astrophys. J., 958(1):48.CrossRefGoogle Scholar
Langfellner, J., Gizon, L., and Birch, A. C. (2015). Spatially resolved vertical vorticity in solar supergranulation using helioseismology and local correlation tracking. Astron. Astrophys., 581:A67.CrossRefGoogle Scholar
Larson, T. P. and Schou, J. (2018). Global–Mode Analysis of Full-Disk Data from the Michelson Doppler Imager and the Helioseismic and Magnetic Imager. Solar Phys., 293(2):29.CrossRefGoogle ScholarPubMed
Lekshmi, B., Gizon, L., Jain, K., Liang, Z.-C., and Philidet, J. (2024). Temporal Variation of Solar Equatorial Rossby Modes with Azimuthal Orders 6 ≤ m ≤ 10. In this volume.Google Scholar
Liang, Z.-C., Gizon, L., Birch, A. C., and Duvall, T. L. (2019). Time-distance helioseismology of solar Rossby waves. Astron. Astrophys., 626:A3.CrossRefGoogle Scholar
Löptien, B., Gizon, L., Birch, A. C., Schou, J., Proxauf, B., Duvall, T. L., Bogart, R. S., and Christensen, U. R. (2018). Global-scale equatorial Rossby waves as an essential component of solar internal dynamics. Nature Astron., 2:568–573.CrossRefGoogle Scholar
Mandal, K., Hanasoge, S. M., and Gizon, L. (2021). Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling. Astron. Astrophys., 652:A96.CrossRefGoogle Scholar
Mandowara, Y., Bekki, Y., and Gizon, L. (2024). Reynolds stress of the m = 1 high latitude inertial mode on the Sun. In this volume.Google Scholar
Matilsky, L. I., Hindman, B. W., Featherstone, N. A., Blume, C. C., and Toomre, J. (2022). Confinement of the Solar Tachocline by Dynamo Action in the Radiative Interior. Astrophys. J., 940(2):L50.CrossRefGoogle Scholar
Miesch, M. S., Brun, A. S., DeRosa, M. L., and Toomre, J. (2008). Structure and Evolution of Giant Cells in Global Models of Solar Convection. Astrophys. J., 673(1):557–575.CrossRefGoogle Scholar
Miesch, M. S., Brun, A. S., and Toomre, J. (2006). Solar Differential Rotation Influenced by Latitudinal Entropy Variations in the Tachocline. Astrophys. J., 641(1):618–625.CrossRefGoogle Scholar
Muñoz-Jaramillo, A., Nandy, D., and Martens, P. C. H. (2011). Magnetic Quenching of Turbulent Diffusivity: Reconciling Mixing-length Theory Estimates with Kinematic Dynamo Models of the Solar Cycle. Astrophys. J., 727(1):L23.CrossRefGoogle Scholar
Philidet, J. and Gizon, L. (2023). Interaction of solar inertial modes with turbulent convection. A 2D model for the excitation of linearly stable modes. Astron. Astrophys., 673:A124.CrossRefGoogle Scholar
Philidet, J. and Gizon, L. (2024). A 2D model for the excitation of the linearly stable inertial modes of the Sun by turbulent convection. In this volume.Google Scholar
Provost, J., Berthomieu, G., and Rocca, A. (1981). Low Frequency Oscillations of a Slowly Rotating Star - Quasi Toroidal Modes. Astron. Astrophys., 94:126.Google Scholar
Proxauf, B. (2021). Observations of large-scale solar flows. PhD thesis, Georg–August-Universität Göttingen, Germany.Google Scholar
Proxauf, B., Gizon, L., Löptien, B., Schou, J., Birch, A. C., and Bogart, R. S. (2020). Exploring the latitude and depth dependence of solar Rossby waves using ring-diagram analysis. Astron. Astrophys., 634:A44.CrossRefGoogle Scholar
Rempel, M. (2005). Solar Differential Rotation and Meridional Flow: The Role of a Subadiabatic Tachocline for the Taylor–Proudman Balance. Astrophys. J., 622(2):1320–1332.CrossRefGoogle Scholar
Triana, S. A., Guerrero, G., Barik, A., and Rekier, J. (2022). Identification of Inertial Modes in the Solar Convection Zone. Astrophys. J., 934(1):L4.CrossRefGoogle Scholar
Ulrich, R. K. (1993). The controversial Sun. In Weiss, W. W. and Baglin, A., editors, IAU Colloq. 137: Inside the Stars, volume 40 of Astron. Soc. Pacific Conf. Ser., page 25.Google Scholar
Ulrich, R. K. (2001). Very Long Lived Wave Patterns Detected in the Solar Surface Velocity Signal. Astrophys. J., 560:466.CrossRefGoogle Scholar
Ulrich, R. K., Boyden, J. E., Webster, L., Snodgrass, H. B., Padilla, S. P., Gilman, P., and Shieber, T. (1988). Solar Rotation Measurements at Mt. Wilson – Part Five. Solar Phys., 117:291.CrossRefGoogle Scholar
Unno, W., Osaki, Y., Ando, H., Saio, H., and Shibahashi, H. (1989). Nonradial oscillations of stars. Tokyo: University of Tokyo Press, 2nd edition.Google Scholar
Verhoeven, J. and Stellmach, S. (2014). The compressional beta effect: A source of zonal winds in planets? Icarus, 237:143–158.CrossRefGoogle Scholar
Waidele, M. and Zhao, J. (2023). Observed Power and Frequency Variations of Solar Rossby Waves with Solar Cycles. Astrophys. J., 954:L26.CrossRefGoogle Scholar
Watson, M. (1981). Shear instability of differential rotation in stars. Geophys. Astrophys. Fluid Dyn., 16:285.CrossRefGoogle Scholar