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

K Mandal,L Gizon,S M Hanasoge

doi:10.1051/0004-6361/202141044

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.

Highlights

Rossby waves are named after their discoverer, Carl-Gustaf Rossby, who first explained the largest scale oscillatory motions on Earth’s atmosphere (Rossby 1939) to arise from the conservation of potential vorticity
Löptien et al (2018) were the first to measure the dispersion relation of these waves in the Sun using surface-granulation tracking methods and ringdiagram analysis with 6 years of SDO/Helioseismic and Magnetic Imager (HMI) data and unambiguously detected modes with azimuthal order starting from t = 3 to t = 15
We only focus on sectoral Rossby modes in this work, as discussed in Sect. 2, and consider the azimuthal order, t = s

Summary

Introduction

Rossby waves are named after their discoverer, Carl-Gustaf Rossby, who first explained the largest scale oscillatory motions on Earth’s atmosphere (Rossby 1939) to arise from the conservation of potential vorticity. Chelton & Schlax (1996) observed these oscillations in the ocean by analyzing variations in the seasurface height from satellite data. Rossby-like waves, known as r-modes in the astrophysical context, can be sustained by any rotating spherical fluid body, such as the Sun, in which the Coriolis force acts as a restoring force (Papaloizou & Pringle 1978; Provost et al 1981; Saio 1982). Löptien et al (2018) were the first to measure the dispersion relation of these waves in the Sun using surface-granulation tracking methods and ringdiagram analysis with 6 years of SDO/Helioseismic and Magnetic Imager (HMI) data and unambiguously detected modes with azimuthal order starting from t = 3 to t = 15. Hanasoge & Mandal (2019) and Mandal & Hanasoge (2020) considered coupling between acoustic modes with the same harmonic degrees They detected Rossby modes only in the sectoral power spectra. We consider couplings between acoustic modes with different harmonic degrees and report the first detection of sectoral Rossby modes with even harmonic degrees using this method

Data analysis

Results

Discussion and conclusions