Detection of Rossby modes with even azimuthal orders using helioseismic normal-mode coupling

Abstract

Context. Retrograde Rossby waves, measured to have significant amplitudes in the Sun, likely have notable implications for various solar phenomena. Aims. Rossby waves create small-amplitude, very-low frequency motions, on the order of the rotation rate and lower, which in turn shift the resonant frequencies and eigenfunctions of the acoustic modes of the Sun. The detection of even azimuthal orders Rossby modes using mode coupling presents additional challenges and prior work therefore only focused on odd orders. Here, we successfully extend the methodology to measure even azimuthal orders as well. Methods. We analyze 4 and 8 years of Helioseismic and Magnetic Imager (HMI) data and consider coupling between different-degree acoustic modes (of separations 1 and 3 in the harmonic degree). The technique uses couplings between different frequency bins to capture the temporal variability of the Rossby modes. Results. We observe significant power close to the theoretical dispersion relation for sectoral Rossby modes, where the azimuthal order is the same as the harmonic degree, s = |t|. Our results are consistent with prior measurements of Rossby modes with azimuthal orders over the range t = 4 to 16 with maximum power occurring at mode t = 8. The amplitudes of these modes vary from 1 to 2 m s−1. We place an upper bound of 0.2 m s−1 on the sectoral t = 2 mode, which we do not detect in our measurements. Conclusions. This effort adds credence to the mode-coupling methodology in helioseismology.

Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation

“…In the solar and stellar context they are also commonly known as r modes (e.g., Papaloizou & Pringle 1978;Saio 1982). The existence of these Rossby modes on the Sun is well established (Löptien et al 2018;Hanasoge & Mandal 2019;Liang et al 2019;Proxauf et al 2020;Mandal & Hanasoge 2020;Hanson et al 2020;Hathaway & Upton 2021;Gizon et al 2021;Mandal et al 2021). They are observed for azimuthal orders in the range 3 ≤ m ≤ 15 and follow the dispersion relation of the classical sectoral (l = m) Rossby modes, where m is the azimuthal order and l is the spherical degree.…”

Radial Trapping of Thermal Rossby Waves within the Convection Zones of Low-mass Stars

“…The unambiguous detection of Rossby waves in the Sun by Löptien et al (2018) has led to a flurry of observational efforts to characterize the waves and to search for other classes of inertial oscillations (e.g., Alshehhi et al 2019;Hanasoge & Mandal 2019;Liang et al 2019;Hanson et al 2020;Proxauf et al 2020;Gizon et al 2021;Hathaway & Upton 2021;Mandal et al 2021). As a result, there has been a resurrection of interest in inertial waves as they might apply to the Sun and solar-like stars (e.g., Lanza et al 2019;Damiani et al 2020;Gizon et al 2020;Cai et al 2021;Bekki et al 2022).…”

Imaging the Sun's near-surface flows using mode-coupling analysis

“…While the derivation of the mode-coupling technique is mathematically challenging, the data analysis is simple and utilizes all the information registered by the mode. Thus far, global mode-coupling has been validated through observations of the meridional flow (Vorontsov 2011;Woodard et al 2013), differential rotation (Schad & Roth 2020;Kashyap et al 2021), global-scale convection (Woodard 2014(Woodard , 2016Hanasoge et al 2020;Mani & Hanasoge 2021) and Rossby modes (Hanasoge & Mandal 2019;Mandal & Hanasoge 2020;Mandal et al 2021). Local mode-coupling analysis in the Cartesian approximation, formulated by Woodard (2006), was validated by Hanson et al (2021) (hereafter H21) by examining the power-spectrum of supergranular waves and comparing with previous time-distance studies (Langfellner et al 2018).…”